Discriminants, resultants, and multidimensional determinants:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1994
|
| Schriftenreihe: | Mathematics: theory & applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 503 - 512 |
| Beschreibung: | X, 523 S. graph. Darst. |
| ISBN: | 3764336609 0817636609 |
Internformat
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Datensatz im Suchindex
| _version_ | 1813502146689105920 |
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I. M. GELFAND M. M. KAPRANOV A. V. ZELEVINSKY DISCRIMINANTS, RESULTANTS,
AND MULTIDIMENSIONAL DETERMINANTS BIRKHAEUSER BOSTON * BASEL * BERLIN
CONTENTS PREFACE IX INTRODUCTION 1 I. GENERAL DISCRIMINANTS AND
RESULTANTS CHAPTER 1. PROJECTIVE DUAL VARIETIES AND GENERAL
DISCRIMINANTS 1. DEFINITIONS AND BASIC EXAMPLES 13 2. DUALITY FOR PLANE
CURVES 16 3. THE INCIDENCE VARIETY AND THE PROOF OF THE BIDUALITY
THEOREM 27 4. FURTHER EXAMPLES AND PROPERTIES OF PROJECTIVE DUALITY 30
5. THE KATZ DIMENSION FORMULA AND ITS APPLICATIONS 39 CHAPTER 2. THE
CAYLEY METHOD FOR STUDYING DISCRIMINANTS 1. JET BUNDLES AND KOSZUL
COMPLEXES 48 2. DISCRIMINANTAL COMPLEXES 54 3. THE DEGREE AND THE
DIMENSION OF THE DUAL 61 4. DISCRIMINANTAL COMPLEXES IN TERMS OF
DIFFERENTIAL FORMS 71 5. THE DISCRIMINANT AS THE DETERMINANT OF A
SPECTRAL SEQUENCE 80 CHAPTER 3. ASSOCIATED VARIETIES AND GENERAL
RESULTANTS 1. GRASSMANNIANS. PRELIMINARY MATERIAL 91 2. ASSOCIATED
HYPERSURFACES 97 3. MIXED RESULTANTS 105 4. THE CAYLEY METHOD FOR THE
STUDY OF RESULTANTS 112 CHAPTER 4. CHOW VARIETIES 1. DEFINITIONS AND
MAIN PROPERTIES 122 2. 0-CYCLES, FACTORIZABLE FORMS AND SYMMETRIE
PRODUCTS 131 3. CAYLEY-GREEN-MORRISON EQUATIONS OF CHOW VARIETIES 146 VI
CONTENTS N. A-DISCRIMINANTS AND A-RESULTANTS CHAPTER 5. TORIC VARIETIES
1. PROJECTIVELY EMBEDDED TORIC VARIETIES 165 2. AFFINE TORIC VARIETIES
AND SEMIGROUPS 172 3. LOCAL STRUCTURE OF TORIC VARIETIES 177 4. ABSTRACT
TORIC VARIETIES AND FANS 187 CHAPTER 6. NEWTON POLYTOPES AND CHOW
POLYTOPES 1. POLYNOMIALS AND THEIR NEWTON POLYTOPES 193 2. THEOREMS OF
KOUCHNIRENKO AND BERNSTEIN ON THE NUMBER OF SOLUTIONS OF A SYSTEM OF
EQUATIONS 200 3. CHOW POLYTOPES 206 CHAPTER 7. TRIANGULATIONS AND
SECONDARY POLYTOPES 1. TRIANGULATIONSAND SECONDARY POLYTOPES 214 2.
FACES OF THE SECONDARY POLYTOPE 227 3. EXAMPLES OF SECONDARY POLYTOPES
233 CHAPTER 8. A-RESULTANTS AND CHOW POLYTOPES OF TORIC VARIETIES 1.
MIXED (AI,.,/\*)-RESULTANTS 252 2. THE A-RESULTANT 255 3. THE CHOW
POLYTOPE OF A TORIC VARIETY AND THE SECONDARY POLYTOPE . . 259 CHAPTER
9. A-DISCRIMINANTS 1. BASIC DEFINITIONS AND EXAMPLES 271 2. THE
DISCRIMINANTAL COMPLEX 275 3. A DIFFERENTIAL-GEOMETRIC CHARACTERIZATION
OF A-DISCRIMINANTAL HYPERSURFACES 285 CHAPTER 10. PRINCIPAL
A-DETERMINANTS 1. STATEMENTS OF MAIN RESULTS 297 2. PROOF OF THE PRIME
FACTORIZATION THEOREM 313 3. PROOF OF THE PROPERTIES OF GENERALIZED
A-DETERMINANTS 329 4. THE PROOF OF THE PRODUCT FORMULA 333 CONTENTS VII
CHAPTER 11. REGULAER A-DETERMINANTS AND A-DISCRIMINANTS 1. DIFFERENTIAL
FORMS ON A SINGULAR TORIC VARIETY AND THE REGULAER A-DETERMINANT 344 2.
NEWTON NUMBERS AND NEWTON FUNCTIONS 351 3. THE NEWTON POLYTOPE OF THE
REGULAER A-DETERMINANT AND OE-EQUIVALENCE OF TRIANGULATIONS 361 4. MORE ON
D-EQUIVALENCE 370 5. RELATIONS TO REAL ALGEBRAIC GEOMETRY 378 DIL
CLASSICAL DISCRIMINANTS AND RESULTANTS CHAPTER 12. DISCRIMINANTS AND
RESULTANTS FOR POLYNOMIALS IN ONE VARIABLE 1. ANOVERVIEWOF CLASSICAL
FORMULAS AND PROPERTIES 397 2. NEWTON POLYTOPES OF THE CLASSICAL
DISCRIMINANT AND RESULTANT . . . . 411 CHAPTER 13. DISCRIMINANTS AND
RESULTANTS FOR FORMS IN SEVERAL VARIABLES 1. HOMOGENEOUS FORMS IN
SEVERAL VARIABLES 426 2. FORMS IN SEVERAL GROUPS OF VARIABLES 437
CHAPTER 14. HYPERDETERMINANTS 1. BASIC PROPERTIES OF THE
HYPERDETERMINANT 444 2. THE CAYLEY METHOD AND THE DEGREE 450 3.
HYPERDETERMINANT OF THE BOUNDARY FORMAT 458 4. SCHLAEFII'S METHOD 475
APPENDIX A. DETERMINANTSOFCOMPLEXES 480 APPENDIX B.A. CAYLEY: ON THE
THEORYOF ELIMINATION 49 8 BIBLIOGRAPHY 503 NOTES AND REFERENCES 513 LIST
OF NOTATIONS 517 INDEX 521 |
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| author | Gelʹfand, Izrailʹ M. 1913-2009 Kapranov, Michail M. 1962- Zelevinskij, Andrej V. |
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| spelling | Gelʹfand, Izrailʹ M. 1913-2009 Verfasser (DE-588)118831364 aut Discriminants, resultants, and multidimensional determinants I. M. Gelfand ; M. M. Kapranov ; A. V. Zelevinsky Boston [u.a.] Birkhäuser 1994 X, 523 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics: theory & applications Literaturverz. S. 503 - 512 Analyse discriminante ram Determinanten gtt Discriminantanalyse gtt Déterminants (Mathématiques) ram Determinants Discriminant analysis Determinante (DE-588)4138983-9 gnd rswk-swf Resultante (DE-588)4177891-1 gnd rswk-swf Diskriminante (DE-588)4150190-1 gnd rswk-swf Diskriminante (DE-588)4150190-1 s DE-604 Resultante (DE-588)4177891-1 s Determinante (DE-588)4138983-9 s Kapranov, Michail M. 1962- Verfasser (DE-588)113769474 aut Zelevinskij, Andrej V. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006421228&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gelʹfand, Izrailʹ M. 1913-2009 Kapranov, Michail M. 1962- Zelevinskij, Andrej V. Discriminants, resultants, and multidimensional determinants Analyse discriminante ram Determinanten gtt Discriminantanalyse gtt Déterminants (Mathématiques) ram Determinants Discriminant analysis Determinante (DE-588)4138983-9 gnd Resultante (DE-588)4177891-1 gnd Diskriminante (DE-588)4150190-1 gnd |
| subject_GND | (DE-588)4138983-9 (DE-588)4177891-1 (DE-588)4150190-1 |
| title | Discriminants, resultants, and multidimensional determinants |
| title_auth | Discriminants, resultants, and multidimensional determinants |
| title_exact_search | Discriminants, resultants, and multidimensional determinants |
| title_full | Discriminants, resultants, and multidimensional determinants I. M. Gelfand ; M. M. Kapranov ; A. V. Zelevinsky |
| title_fullStr | Discriminants, resultants, and multidimensional determinants I. M. Gelfand ; M. M. Kapranov ; A. V. Zelevinsky |
| title_full_unstemmed | Discriminants, resultants, and multidimensional determinants I. M. Gelfand ; M. M. Kapranov ; A. V. Zelevinsky |
| title_short | Discriminants, resultants, and multidimensional determinants |
| title_sort | discriminants resultants and multidimensional determinants |
| topic | Analyse discriminante ram Determinanten gtt Discriminantanalyse gtt Déterminants (Mathématiques) ram Determinants Discriminant analysis Determinante (DE-588)4138983-9 gnd Resultante (DE-588)4177891-1 gnd Diskriminante (DE-588)4150190-1 gnd |
| topic_facet | Analyse discriminante Determinanten Discriminantanalyse Déterminants (Mathématiques) Determinants Discriminant analysis Determinante Resultante Diskriminante |
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