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Titel:	Discriminants, resultants, and multidimensional determinants
Von:	I. M. Gelfand ; M. M. Kapranov ; A. V. Zelevinsky
Person:	Gelʹfand, Izrailʹ M. 1913-2009 Verfasser aut Kapranov, Michail M. Zelevinskij, Andrej V. 1962-
Hauptverfassende:	Gelʹfand, Izrailʹ M. 1913-2009 (VerfasserIn), Kapranov, Michail M. 1962- (VerfasserIn), Zelevinskij, Andrej V. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Boston [u.a.] Birkhäuser 1994
Schriftenreihe:	Mathematics: theory & applications
Notation:	SK 240
Schlagwörter:	Analyse discriminante Determinanten Discriminantanalyse Déterminants (Mathématiques) Determinants Discriminant analysis Diskriminante Determinante Resultante
Medienzugang:	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
Beschreibung:	Literaturverz. S. 503 - 512
Umfang:	X, 523 S. graph. Darst.
ISBN:	3764336609 0817636609

Internformat

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adam_text	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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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 Diskriminante (DE-588)4150190-1 gnd Determinante (DE-588)4138983-9 gnd Resultante (DE-588)4177891-1 gnd
subject_GND	(DE-588)4150190-1 (DE-588)4138983-9 (DE-588)4177891-1
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 Diskriminante (DE-588)4150190-1 gnd Determinante (DE-588)4138983-9 gnd Resultante (DE-588)4177891-1 gnd
topic_facet	Analyse discriminante Determinanten Discriminantanalyse Déterminants (Mathématiques) Determinants Discriminant analysis Diskriminante Determinante Resultante
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