Algebraic curves over a finite field /:
This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correctin...
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| Hauptverfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, New Jersey :
Princeton University Press,
2008.
|
| Schriftenreihe: | Princeton series in applied mathematics.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristi. |
| Beschreibung: | 1 online resource (717 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781400847419 1400847419 1306988608 9781306988605 9781400847426 1400847427 0691096791 9780691096797 |
Internformat
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| 100 | 1 | |a Hirschfeld, J. W. P. |q (James William Peter), |d 1940- |e author. |1 https://id.oclc.org/worldcat/entity/E39PBJk964cfBXQTGmTTp4gqcP |0 http://id.loc.gov/authorities/names/n81072707 | |
| 245 | 1 | 0 | |a Algebraic curves over a finite field / |c J.W.P. Hirschfeld, G. Korchmaros, F. Torres. |
| 264 | 1 | |a Princeton, New Jersey : |b Princeton University Press, |c 2008. | |
| 264 | 4 | |c ©2008 | |
| 300 | |a 1 online resource (717 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 353 | |a bibliography |b bibliography | ||
| 353 | |a index |b index | ||
| 490 | 1 | |a Princeton Series in Applied Mathematics | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. GENERAL THEORY OF CURVES; Chapter 1. Fundamental ideas; 1.1 Basic definitions; 1.2 Polynomials; 1.3 Affine plane curves; 1.4 Projective plane curves; 1.5 The Hessian curve; 1.6 Projective varieties in higher-dimensional spaces; 1.7 Exercises; 1.8 Notes; Chapter 2. Elimination theory; 2.1 Elimination of one unknown; 2.2 The discriminant; 2.3 Elimination in a system in two unknowns; 2.4 Exercises; 2.5 Notes; Chapter 3. Singular points and intersections; 3.1 The intersection number of two curves; 3.2 Bézout's Theorem. | |
| 505 | 8 | |a 3.3 Rational and birational transformations3.4 Quadratic transformations; 3.5 Resolution of singularities; 3.6 Exercises; 3.7 Notes; Chapter 4. Branches and parametrisation; 4.1 Formal power series; 4.2 Branch representations; 4.3 Branches of plane algebraic curves; 4.4 Local quadratic transformations; 4.5 Noether's Theorem; 4.6 Analytic branches; 4.7 Exercises; 4.8 Notes; Chapter 5. The function field of a curve; 5.1 Generic points; 5.2 Rational transformations; 5.3 Places; 5.4 Zeros and poles; 5.5 Separability and inseparability; 5.6 Frobenius rational transformations. | |
| 505 | 8 | |a 5.7 Derivations and differentials5.8 The genus of a curve; 5.9 Residues of differential forms; 5.10 Higher derivatives in positive characteristic; 5.11 The dual and bidual of a curve; 5.12 Exercises; 5.13 Notes; Chapter 6. Linear series and the Riemann-Roch Theorem; 6.1 Divisors and linear series; 6.2 Linear systems of curves; 6.3 Special and non-special linear series; 6.4 Reformulation of the Riemann-Roch Theorem; 6.5 Some consequences of the Riemann-Roch Theorem; 6.6 The Weierstrass Gap Theorem; 6.7 The structure of the divisor class group; 6.8 Exercises; 6.9 Notes. | |
| 505 | 8 | |a Chapter 7. Algebraic curves in higher-dimensional spaces7.1 Basic definitions and properties; 7.2 Rational transformations; 7.3 Hurwitz's Theorem; 7.4 Linear series composed of an involution; 7.5 The canonical curve; 7.6 Osculating hyperplanes and ramification divisors; 7.7 Non-classical curves and linear systems of lines; 7.8 Non-classical curves and linear systems of conics; 7.9 Dual curves of space curves; 7.10 Complete linear series of small order; 7.11 Examples of curves; 7.12 The Linear General Position Principle; 7.13 Castelnuovo's Bound; 7.14 A generalisation of Clifford's Theorem. | |
| 505 | 8 | |a 7.15 The Uniform Position Principle7.16 Valuation rings; 7.17 Curves as algebraic varieties of dimension one; 7.18 Exercises; 7.19 Notes; PART 2. CURVES OVER A FINITE FIELD; Chapter 8. Rational points and places over a finite field; 8.1 Plane curves defined over a finite field; 8.2 Fq-rational branches of a curve; 8.3 Fq-rational places, divisors and linear series; 8.4 Space curves over Fq; 8.5 The Stöhr-Voloch Theorem; 8.6 Frobenius classicality with respect to lines; 8.7 Frobenius classicality with respect to conics; 8.8 The dual of a Frobenius non-classical curve; 8.9 Exercises; 8.10 Notes. | |
| 520 | |a This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristi. | ||
| 546 | |a In English. | ||
| 650 | 0 | |a Curves, Algebraic. |0 http://id.loc.gov/authorities/subjects/sh85034916 | |
| 650 | 0 | |a Finite fields (Algebra) |0 http://id.loc.gov/authorities/subjects/sh85048351 | |
| 650 | 6 | |a Courbes algébriques. | |
| 650 | 6 | |a Corps finis. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x General. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Abstract. |2 bisacsh | |
| 650 | 7 | |a Curves, Algebraic |2 fast | |
| 650 | 7 | |a Finite fields (Algebra) |2 fast | |
| 650 | 7 | |a Galois-Feld |2 gnd |0 http://d-nb.info/gnd/4155896-0 | |
| 650 | 7 | |a Algebraische Kurve |2 gnd |0 http://d-nb.info/gnd/4001165-3 | |
| 700 | 1 | |a Korchmáros, G., |e author. | |
| 700 | 1 | |a Torres, F. |q (Fernando), |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjD8cm4CPFVqw7qR4c79wC |0 http://id.loc.gov/authorities/names/no2014070081 | |
| 758 | |i has work: |a Algebraic curves over a finite field (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFXdPJgCQHxwgrXpdxFPcd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Hirschfeld, J.W.P. (James William Peter), 1940- |t Algebraic curves over a finite field. |d Princeton, New Jersey : Princeton University Press, ©2008 |h xx, 696 pages |k Princeton series in applied mathematics. |z 9780691096797 |
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| author | Hirschfeld, J. W. P. (James William Peter), 1940- Korchmáros, G. Torres, F. (Fernando) |
| author_GND | http://id.loc.gov/authorities/names/n81072707 http://id.loc.gov/authorities/names/no2014070081 |
| author_facet | Hirschfeld, J. W. P. (James William Peter), 1940- Korchmáros, G. Torres, F. (Fernando) |
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| contents | Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. GENERAL THEORY OF CURVES; Chapter 1. Fundamental ideas; 1.1 Basic definitions; 1.2 Polynomials; 1.3 Affine plane curves; 1.4 Projective plane curves; 1.5 The Hessian curve; 1.6 Projective varieties in higher-dimensional spaces; 1.7 Exercises; 1.8 Notes; Chapter 2. Elimination theory; 2.1 Elimination of one unknown; 2.2 The discriminant; 2.3 Elimination in a system in two unknowns; 2.4 Exercises; 2.5 Notes; Chapter 3. Singular points and intersections; 3.1 The intersection number of two curves; 3.2 Bézout's Theorem. 3.3 Rational and birational transformations3.4 Quadratic transformations; 3.5 Resolution of singularities; 3.6 Exercises; 3.7 Notes; Chapter 4. Branches and parametrisation; 4.1 Formal power series; 4.2 Branch representations; 4.3 Branches of plane algebraic curves; 4.4 Local quadratic transformations; 4.5 Noether's Theorem; 4.6 Analytic branches; 4.7 Exercises; 4.8 Notes; Chapter 5. The function field of a curve; 5.1 Generic points; 5.2 Rational transformations; 5.3 Places; 5.4 Zeros and poles; 5.5 Separability and inseparability; 5.6 Frobenius rational transformations. 5.7 Derivations and differentials5.8 The genus of a curve; 5.9 Residues of differential forms; 5.10 Higher derivatives in positive characteristic; 5.11 The dual and bidual of a curve; 5.12 Exercises; 5.13 Notes; Chapter 6. Linear series and the Riemann-Roch Theorem; 6.1 Divisors and linear series; 6.2 Linear systems of curves; 6.3 Special and non-special linear series; 6.4 Reformulation of the Riemann-Roch Theorem; 6.5 Some consequences of the Riemann-Roch Theorem; 6.6 The Weierstrass Gap Theorem; 6.7 The structure of the divisor class group; 6.8 Exercises; 6.9 Notes. Chapter 7. Algebraic curves in higher-dimensional spaces7.1 Basic definitions and properties; 7.2 Rational transformations; 7.3 Hurwitz's Theorem; 7.4 Linear series composed of an involution; 7.5 The canonical curve; 7.6 Osculating hyperplanes and ramification divisors; 7.7 Non-classical curves and linear systems of lines; 7.8 Non-classical curves and linear systems of conics; 7.9 Dual curves of space curves; 7.10 Complete linear series of small order; 7.11 Examples of curves; 7.12 The Linear General Position Principle; 7.13 Castelnuovo's Bound; 7.14 A generalisation of Clifford's Theorem. 7.15 The Uniform Position Principle7.16 Valuation rings; 7.17 Curves as algebraic varieties of dimension one; 7.18 Exercises; 7.19 Notes; PART 2. CURVES OVER A FINITE FIELD; Chapter 8. Rational points and places over a finite field; 8.1 Plane curves defined over a finite field; 8.2 Fq-rational branches of a curve; 8.3 Fq-rational places, divisors and linear series; 8.4 Space curves over Fq; 8.5 The Stöhr-Voloch Theorem; 8.6 Frobenius classicality with respect to lines; 8.7 Frobenius classicality with respect to conics; 8.8 The dual of a Frobenius non-classical curve; 8.9 Exercises; 8.10 Notes. |
| ctrlnum | (OCoLC)889240929 |
| dewey-full | 516.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.352 |
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| discipline | Mathematik |
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GENERAL THEORY OF CURVES; Chapter 1. Fundamental ideas; 1.1 Basic definitions; 1.2 Polynomials; 1.3 Affine plane curves; 1.4 Projective plane curves; 1.5 The Hessian curve; 1.6 Projective varieties in higher-dimensional spaces; 1.7 Exercises; 1.8 Notes; Chapter 2. Elimination theory; 2.1 Elimination of one unknown; 2.2 The discriminant; 2.3 Elimination in a system in two unknowns; 2.4 Exercises; 2.5 Notes; Chapter 3. Singular points and intersections; 3.1 The intersection number of two curves; 3.2 Bézout's Theorem.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3.3 Rational and birational transformations3.4 Quadratic transformations; 3.5 Resolution of singularities; 3.6 Exercises; 3.7 Notes; Chapter 4. Branches and parametrisation; 4.1 Formal power series; 4.2 Branch representations; 4.3 Branches of plane algebraic curves; 4.4 Local quadratic transformations; 4.5 Noether's Theorem; 4.6 Analytic branches; 4.7 Exercises; 4.8 Notes; Chapter 5. The function field of a curve; 5.1 Generic points; 5.2 Rational transformations; 5.3 Places; 5.4 Zeros and poles; 5.5 Separability and inseparability; 5.6 Frobenius rational transformations.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">5.7 Derivations and differentials5.8 The genus of a curve; 5.9 Residues of differential forms; 5.10 Higher derivatives in positive characteristic; 5.11 The dual and bidual of a curve; 5.12 Exercises; 5.13 Notes; Chapter 6. Linear series and the Riemann-Roch Theorem; 6.1 Divisors and linear series; 6.2 Linear systems of curves; 6.3 Special and non-special linear series; 6.4 Reformulation of the Riemann-Roch Theorem; 6.5 Some consequences of the Riemann-Roch Theorem; 6.6 The Weierstrass Gap Theorem; 6.7 The structure of the divisor class group; 6.8 Exercises; 6.9 Notes.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Chapter 7. Algebraic curves in higher-dimensional spaces7.1 Basic definitions and properties; 7.2 Rational transformations; 7.3 Hurwitz's Theorem; 7.4 Linear series composed of an involution; 7.5 The canonical curve; 7.6 Osculating hyperplanes and ramification divisors; 7.7 Non-classical curves and linear systems of lines; 7.8 Non-classical curves and linear systems of conics; 7.9 Dual curves of space curves; 7.10 Complete linear series of small order; 7.11 Examples of curves; 7.12 The Linear General Position Principle; 7.13 Castelnuovo's Bound; 7.14 A generalisation of Clifford's Theorem.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">7.15 The Uniform Position Principle7.16 Valuation rings; 7.17 Curves as algebraic varieties of dimension one; 7.18 Exercises; 7.19 Notes; PART 2. CURVES OVER A FINITE FIELD; Chapter 8. Rational points and places over a finite field; 8.1 Plane curves defined over a finite field; 8.2 Fq-rational branches of a curve; 8.3 Fq-rational places, divisors and linear series; 8.4 Space curves over Fq; 8.5 The Stöhr-Voloch Theorem; 8.6 Frobenius classicality with respect to lines; 8.7 Frobenius classicality with respect to conics; 8.8 The dual of a Frobenius non-classical curve; 8.9 Exercises; 8.10 Notes.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. 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| id | ZDB-4-EBA-ocn889240929 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:26:09Z |
| institution | BVB |
| isbn | 9781400847419 1400847419 1306988608 9781306988605 9781400847426 1400847427 0691096791 9780691096797 |
| language | English |
| oclc_num | 889240929 |
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| physical | 1 online resource (717 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | Princeton University Press, |
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| series | Princeton series in applied mathematics. |
| series2 | Princeton Series in Applied Mathematics |
| spelling | Hirschfeld, J. W. P. (James William Peter), 1940- author. https://id.oclc.org/worldcat/entity/E39PBJk964cfBXQTGmTTp4gqcP http://id.loc.gov/authorities/names/n81072707 Algebraic curves over a finite field / J.W.P. Hirschfeld, G. Korchmaros, F. Torres. Princeton, New Jersey : Princeton University Press, 2008. ©2008 1 online resource (717 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file bibliography bibliography index index Princeton Series in Applied Mathematics Includes bibliographical references and index. Print version record. Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. GENERAL THEORY OF CURVES; Chapter 1. Fundamental ideas; 1.1 Basic definitions; 1.2 Polynomials; 1.3 Affine plane curves; 1.4 Projective plane curves; 1.5 The Hessian curve; 1.6 Projective varieties in higher-dimensional spaces; 1.7 Exercises; 1.8 Notes; Chapter 2. Elimination theory; 2.1 Elimination of one unknown; 2.2 The discriminant; 2.3 Elimination in a system in two unknowns; 2.4 Exercises; 2.5 Notes; Chapter 3. Singular points and intersections; 3.1 The intersection number of two curves; 3.2 Bézout's Theorem. 3.3 Rational and birational transformations3.4 Quadratic transformations; 3.5 Resolution of singularities; 3.6 Exercises; 3.7 Notes; Chapter 4. Branches and parametrisation; 4.1 Formal power series; 4.2 Branch representations; 4.3 Branches of plane algebraic curves; 4.4 Local quadratic transformations; 4.5 Noether's Theorem; 4.6 Analytic branches; 4.7 Exercises; 4.8 Notes; Chapter 5. The function field of a curve; 5.1 Generic points; 5.2 Rational transformations; 5.3 Places; 5.4 Zeros and poles; 5.5 Separability and inseparability; 5.6 Frobenius rational transformations. 5.7 Derivations and differentials5.8 The genus of a curve; 5.9 Residues of differential forms; 5.10 Higher derivatives in positive characteristic; 5.11 The dual and bidual of a curve; 5.12 Exercises; 5.13 Notes; Chapter 6. Linear series and the Riemann-Roch Theorem; 6.1 Divisors and linear series; 6.2 Linear systems of curves; 6.3 Special and non-special linear series; 6.4 Reformulation of the Riemann-Roch Theorem; 6.5 Some consequences of the Riemann-Roch Theorem; 6.6 The Weierstrass Gap Theorem; 6.7 The structure of the divisor class group; 6.8 Exercises; 6.9 Notes. Chapter 7. Algebraic curves in higher-dimensional spaces7.1 Basic definitions and properties; 7.2 Rational transformations; 7.3 Hurwitz's Theorem; 7.4 Linear series composed of an involution; 7.5 The canonical curve; 7.6 Osculating hyperplanes and ramification divisors; 7.7 Non-classical curves and linear systems of lines; 7.8 Non-classical curves and linear systems of conics; 7.9 Dual curves of space curves; 7.10 Complete linear series of small order; 7.11 Examples of curves; 7.12 The Linear General Position Principle; 7.13 Castelnuovo's Bound; 7.14 A generalisation of Clifford's Theorem. 7.15 The Uniform Position Principle7.16 Valuation rings; 7.17 Curves as algebraic varieties of dimension one; 7.18 Exercises; 7.19 Notes; PART 2. CURVES OVER A FINITE FIELD; Chapter 8. Rational points and places over a finite field; 8.1 Plane curves defined over a finite field; 8.2 Fq-rational branches of a curve; 8.3 Fq-rational places, divisors and linear series; 8.4 Space curves over Fq; 8.5 The Stöhr-Voloch Theorem; 8.6 Frobenius classicality with respect to lines; 8.7 Frobenius classicality with respect to conics; 8.8 The dual of a Frobenius non-classical curve; 8.9 Exercises; 8.10 Notes. This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristi. In English. Curves, Algebraic. http://id.loc.gov/authorities/subjects/sh85034916 Finite fields (Algebra) http://id.loc.gov/authorities/subjects/sh85048351 Courbes algébriques. Corps finis. MATHEMATICS Geometry General. bisacsh MATHEMATICS Algebra Abstract. bisacsh Curves, Algebraic fast Finite fields (Algebra) fast Galois-Feld gnd http://d-nb.info/gnd/4155896-0 Algebraische Kurve gnd http://d-nb.info/gnd/4001165-3 Korchmáros, G., author. Torres, F. (Fernando), author. https://id.oclc.org/worldcat/entity/E39PCjD8cm4CPFVqw7qR4c79wC http://id.loc.gov/authorities/names/no2014070081 has work: Algebraic curves over a finite field (Text) https://id.oclc.org/worldcat/entity/E39PCFXdPJgCQHxwgrXpdxFPcd https://id.oclc.org/worldcat/ontology/hasWork Print version: Hirschfeld, J.W.P. (James William Peter), 1940- Algebraic curves over a finite field. Princeton, New Jersey : Princeton University Press, ©2008 xx, 696 pages Princeton series in applied mathematics. 9780691096797 Princeton series in applied mathematics. http://id.loc.gov/authorities/names/no2002046464 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=816476 Volltext |
| spellingShingle | Hirschfeld, J. W. P. (James William Peter), 1940- Korchmáros, G. Torres, F. (Fernando) Algebraic curves over a finite field / Princeton series in applied mathematics. Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. GENERAL THEORY OF CURVES; Chapter 1. Fundamental ideas; 1.1 Basic definitions; 1.2 Polynomials; 1.3 Affine plane curves; 1.4 Projective plane curves; 1.5 The Hessian curve; 1.6 Projective varieties in higher-dimensional spaces; 1.7 Exercises; 1.8 Notes; Chapter 2. Elimination theory; 2.1 Elimination of one unknown; 2.2 The discriminant; 2.3 Elimination in a system in two unknowns; 2.4 Exercises; 2.5 Notes; Chapter 3. Singular points and intersections; 3.1 The intersection number of two curves; 3.2 Bézout's Theorem. 3.3 Rational and birational transformations3.4 Quadratic transformations; 3.5 Resolution of singularities; 3.6 Exercises; 3.7 Notes; Chapter 4. Branches and parametrisation; 4.1 Formal power series; 4.2 Branch representations; 4.3 Branches of plane algebraic curves; 4.4 Local quadratic transformations; 4.5 Noether's Theorem; 4.6 Analytic branches; 4.7 Exercises; 4.8 Notes; Chapter 5. The function field of a curve; 5.1 Generic points; 5.2 Rational transformations; 5.3 Places; 5.4 Zeros and poles; 5.5 Separability and inseparability; 5.6 Frobenius rational transformations. 5.7 Derivations and differentials5.8 The genus of a curve; 5.9 Residues of differential forms; 5.10 Higher derivatives in positive characteristic; 5.11 The dual and bidual of a curve; 5.12 Exercises; 5.13 Notes; Chapter 6. Linear series and the Riemann-Roch Theorem; 6.1 Divisors and linear series; 6.2 Linear systems of curves; 6.3 Special and non-special linear series; 6.4 Reformulation of the Riemann-Roch Theorem; 6.5 Some consequences of the Riemann-Roch Theorem; 6.6 The Weierstrass Gap Theorem; 6.7 The structure of the divisor class group; 6.8 Exercises; 6.9 Notes. Chapter 7. Algebraic curves in higher-dimensional spaces7.1 Basic definitions and properties; 7.2 Rational transformations; 7.3 Hurwitz's Theorem; 7.4 Linear series composed of an involution; 7.5 The canonical curve; 7.6 Osculating hyperplanes and ramification divisors; 7.7 Non-classical curves and linear systems of lines; 7.8 Non-classical curves and linear systems of conics; 7.9 Dual curves of space curves; 7.10 Complete linear series of small order; 7.11 Examples of curves; 7.12 The Linear General Position Principle; 7.13 Castelnuovo's Bound; 7.14 A generalisation of Clifford's Theorem. 7.15 The Uniform Position Principle7.16 Valuation rings; 7.17 Curves as algebraic varieties of dimension one; 7.18 Exercises; 7.19 Notes; PART 2. CURVES OVER A FINITE FIELD; Chapter 8. Rational points and places over a finite field; 8.1 Plane curves defined over a finite field; 8.2 Fq-rational branches of a curve; 8.3 Fq-rational places, divisors and linear series; 8.4 Space curves over Fq; 8.5 The Stöhr-Voloch Theorem; 8.6 Frobenius classicality with respect to lines; 8.7 Frobenius classicality with respect to conics; 8.8 The dual of a Frobenius non-classical curve; 8.9 Exercises; 8.10 Notes. Curves, Algebraic. http://id.loc.gov/authorities/subjects/sh85034916 Finite fields (Algebra) http://id.loc.gov/authorities/subjects/sh85048351 Courbes algébriques. Corps finis. MATHEMATICS Geometry General. bisacsh MATHEMATICS Algebra Abstract. bisacsh Curves, Algebraic fast Finite fields (Algebra) fast Galois-Feld gnd http://d-nb.info/gnd/4155896-0 Algebraische Kurve gnd http://d-nb.info/gnd/4001165-3 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85034916 http://id.loc.gov/authorities/subjects/sh85048351 http://d-nb.info/gnd/4155896-0 http://d-nb.info/gnd/4001165-3 |
| title | Algebraic curves over a finite field / |
| title_auth | Algebraic curves over a finite field / |
| title_exact_search | Algebraic curves over a finite field / |
| title_full | Algebraic curves over a finite field / J.W.P. Hirschfeld, G. Korchmaros, F. Torres. |
| title_fullStr | Algebraic curves over a finite field / J.W.P. Hirschfeld, G. Korchmaros, F. Torres. |
| title_full_unstemmed | Algebraic curves over a finite field / J.W.P. Hirschfeld, G. Korchmaros, F. Torres. |
| title_short | Algebraic curves over a finite field / |
| title_sort | algebraic curves over a finite field |
| topic | Curves, Algebraic. http://id.loc.gov/authorities/subjects/sh85034916 Finite fields (Algebra) http://id.loc.gov/authorities/subjects/sh85048351 Courbes algébriques. Corps finis. MATHEMATICS Geometry General. bisacsh MATHEMATICS Algebra Abstract. bisacsh Curves, Algebraic fast Finite fields (Algebra) fast Galois-Feld gnd http://d-nb.info/gnd/4155896-0 Algebraische Kurve gnd http://d-nb.info/gnd/4001165-3 |
| topic_facet | Curves, Algebraic. Finite fields (Algebra) Courbes algébriques. Corps finis. MATHEMATICS Geometry General. MATHEMATICS Algebra Abstract. Curves, Algebraic Galois-Feld Algebraische Kurve |
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