Complex algebraic curves /:
Complex algebraic curves were developed in the nineteenth century. They have many fascinating properties and crop up in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired by most undergraduate cou...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1992.
|
| Schriftenreihe: | London Mathematical Society student texts ;
23. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Complex algebraic curves were developed in the nineteenth century. They have many fascinating properties and crop up in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired by most undergraduate courses in mathematics, Dr Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis. This book grew from a lecture course given by Dr Kirwan at Oxford University and will be an excellent companion for final year undergraduates and graduates who are studying complex algebraic curves. |
| Beschreibung: | 1 online resource (viii, 264 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 259-261) and index. |
| ISBN: | 9780511623929 0511623925 9781107088276 1107088275 9781107094499 1107094496 |
Internformat
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| 245 | 1 | 0 | |a Complex algebraic curves / |c Frances Kirwan. |
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| 505 | 0 | |a A brief history of algebraic curves -- Relationship with other parts of mathematics -- Number theory -- Singularities and the theory of knots -- Complex analysis -- Abelian integrals -- Real Algebraic Curves -- Hilbert's Nullstellensatz -- Techniques for drawing real algebraic curves -- Real algebraic curves inside complex algebraic curves -- Important examples of real algebraic curves -- Foundations -- Complex algebraic curves in C[superscript 2] -- Complex projective spaces -- Complex projective curves in P[subscript 2] -- Affine and projective curves -- Algebraic properties -- Bezout's theorem -- Points of inflection and cubic curves -- Topological properties -- The degree-genus formula -- The first method of proof -- The second method of proof -- Branched covers of P[subscript 1] -- Proof of the degree-genus formula -- Riemann surfaces -- The Weierstrass [weierp]-function -- Riemann surfaces -- Differentials on Riemann surfaces -- Holomorphic differentials -- Abel's theorem -- The Riemann-Roch theorem -- Singular curves -- Resolution of singularities -- Newton polygons and Puiseux expansions -- The topology of singular curves -- Algebra -- Complex analysis -- Topology -- Covering projections -- The genus is a topological invariant -- Spheres with handles. | |
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| author | Kirwan, Frances Clare, 1959- |
| author_GND | http://id.loc.gov/authorities/names/n84077096 |
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| contents | A brief history of algebraic curves -- Relationship with other parts of mathematics -- Number theory -- Singularities and the theory of knots -- Complex analysis -- Abelian integrals -- Real Algebraic Curves -- Hilbert's Nullstellensatz -- Techniques for drawing real algebraic curves -- Real algebraic curves inside complex algebraic curves -- Important examples of real algebraic curves -- Foundations -- Complex algebraic curves in C[superscript 2] -- Complex projective spaces -- Complex projective curves in P[subscript 2] -- Affine and projective curves -- Algebraic properties -- Bezout's theorem -- Points of inflection and cubic curves -- Topological properties -- The degree-genus formula -- The first method of proof -- The second method of proof -- Branched covers of P[subscript 1] -- Proof of the degree-genus formula -- Riemann surfaces -- The Weierstrass [weierp]-function -- Riemann surfaces -- Differentials on Riemann surfaces -- Holomorphic differentials -- Abel's theorem -- The Riemann-Roch theorem -- Singular curves -- Resolution of singularities -- Newton polygons and Puiseux expansions -- The topology of singular curves -- Algebra -- Complex analysis -- Topology -- Covering projections -- The genus is a topological invariant -- Spheres with handles. |
| ctrlnum | (OCoLC)818223081 |
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| genre | Electronic book. |
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| id | ZDB-4-EBA-ocn818223081 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:03Z |
| institution | BVB |
| isbn | 9780511623929 0511623925 9781107088276 1107088275 9781107094499 1107094496 |
| language | English |
| oclc_num | 818223081 |
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| physical | 1 online resource (viii, 264 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Cambridge University Press, |
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| series | London Mathematical Society student texts ; |
| series2 | London Mathematical Society student texts ; |
| spelling | Kirwan, Frances Clare, 1959- https://id.oclc.org/worldcat/entity/E39PBJtxmFpxXvBTvHd6MbTGpP http://id.loc.gov/authorities/names/n84077096 Complex algebraic curves / Frances Kirwan. Cambridge ; New York : Cambridge University Press, 1992. 1 online resource (viii, 264 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society student texts ; 23 Includes bibliographical references (pages 259-261) and index. Print version record. Complex algebraic curves were developed in the nineteenth century. They have many fascinating properties and crop up in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired by most undergraduate courses in mathematics, Dr Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis. This book grew from a lecture course given by Dr Kirwan at Oxford University and will be an excellent companion for final year undergraduates and graduates who are studying complex algebraic curves. A brief history of algebraic curves -- Relationship with other parts of mathematics -- Number theory -- Singularities and the theory of knots -- Complex analysis -- Abelian integrals -- Real Algebraic Curves -- Hilbert's Nullstellensatz -- Techniques for drawing real algebraic curves -- Real algebraic curves inside complex algebraic curves -- Important examples of real algebraic curves -- Foundations -- Complex algebraic curves in C[superscript 2] -- Complex projective spaces -- Complex projective curves in P[subscript 2] -- Affine and projective curves -- Algebraic properties -- Bezout's theorem -- Points of inflection and cubic curves -- Topological properties -- The degree-genus formula -- The first method of proof -- The second method of proof -- Branched covers of P[subscript 1] -- Proof of the degree-genus formula -- Riemann surfaces -- The Weierstrass [weierp]-function -- Riemann surfaces -- Differentials on Riemann surfaces -- Holomorphic differentials -- Abel's theorem -- The Riemann-Roch theorem -- Singular curves -- Resolution of singularities -- Newton polygons and Puiseux expansions -- The topology of singular curves -- Algebra -- Complex analysis -- Topology -- Covering projections -- The genus is a topological invariant -- Spheres with handles. Curves, Algebraic. http://id.loc.gov/authorities/subjects/sh85034916 Courbes algébriques. MATHEMATICS Geometry Algebraic. bisacsh Curves, Algebraic fast Komplexe algebraische Kurve gnd http://d-nb.info/gnd/4164890-0 Courbes algébriques. ram Electronic book. Print version: Kirwan, Frances Clare, 1959- Complex algebraic curves. Cambridge ; New York : Cambridge University Press, 1992 052141251X (DLC) 92192303 (OCoLC)25576801 London Mathematical Society student texts ; 23. http://id.loc.gov/authorities/names/n84727069 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=570488 Volltext |
| spellingShingle | Kirwan, Frances Clare, 1959- Complex algebraic curves / London Mathematical Society student texts ; A brief history of algebraic curves -- Relationship with other parts of mathematics -- Number theory -- Singularities and the theory of knots -- Complex analysis -- Abelian integrals -- Real Algebraic Curves -- Hilbert's Nullstellensatz -- Techniques for drawing real algebraic curves -- Real algebraic curves inside complex algebraic curves -- Important examples of real algebraic curves -- Foundations -- Complex algebraic curves in C[superscript 2] -- Complex projective spaces -- Complex projective curves in P[subscript 2] -- Affine and projective curves -- Algebraic properties -- Bezout's theorem -- Points of inflection and cubic curves -- Topological properties -- The degree-genus formula -- The first method of proof -- The second method of proof -- Branched covers of P[subscript 1] -- Proof of the degree-genus formula -- Riemann surfaces -- The Weierstrass [weierp]-function -- Riemann surfaces -- Differentials on Riemann surfaces -- Holomorphic differentials -- Abel's theorem -- The Riemann-Roch theorem -- Singular curves -- Resolution of singularities -- Newton polygons and Puiseux expansions -- The topology of singular curves -- Algebra -- Complex analysis -- Topology -- Covering projections -- The genus is a topological invariant -- Spheres with handles. Curves, Algebraic. http://id.loc.gov/authorities/subjects/sh85034916 Courbes algébriques. MATHEMATICS Geometry Algebraic. bisacsh Curves, Algebraic fast Komplexe algebraische Kurve gnd http://d-nb.info/gnd/4164890-0 Courbes algébriques. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85034916 http://d-nb.info/gnd/4164890-0 |
| title | Complex algebraic curves / |
| title_auth | Complex algebraic curves / |
| title_exact_search | Complex algebraic curves / |
| title_full | Complex algebraic curves / Frances Kirwan. |
| title_fullStr | Complex algebraic curves / Frances Kirwan. |
| title_full_unstemmed | Complex algebraic curves / Frances Kirwan. |
| title_short | Complex algebraic curves / |
| title_sort | complex algebraic curves |
| topic | Curves, Algebraic. http://id.loc.gov/authorities/subjects/sh85034916 Courbes algébriques. MATHEMATICS Geometry Algebraic. bisacsh Curves, Algebraic fast Komplexe algebraische Kurve gnd http://d-nb.info/gnd/4164890-0 Courbes algébriques. ram |
| topic_facet | Curves, Algebraic. Courbes algébriques. MATHEMATICS Geometry Algebraic. Curves, Algebraic Komplexe algebraische Kurve Electronic book. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=570488 |
| work_keys_str_mv | AT kirwanfrancesclare complexalgebraiccurves |