Discriminants, resultants and multidimensional determinants:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2008
|
| Edition: | Reprint of the 1994 ed. |
| Series: | Modern Birkhäuser classics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 523 S. graph. Darst. |
| ISBN: | 9780817647704 |
Staff View
MARC
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| 245 | 1 | 0 | |a Discriminants, resultants and multidimensional determinants |c I. M. Gelfand ; M. M. Kapranov ; A. V. Zelevinsky |
| 250 | |a Reprint of the 1994 ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2008 | |
| 300 | |a X, 523 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 700 | 1 | |a Zelevinskij, Andrej V. |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1813502146706931712 |
|---|---|
| adam_text |
Contents
Preface
їх
Introduction
. 1
L 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.
O-cycles, factorizable forms and symmetric products
. 131
3.
Cay ley-Green-Morrison equations of Chow varieties
. 146
vi
Contents
IL A-DISCRIMINANTS AND A-RESULTANTS
CHAPTER
5.
Tone Varieties
1.
Protectively embedded tone 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.
Triangulations
and secondary polytopes
. 214
2.
Faces of the secondary polytope
. 227
3.
Examples of secondary polytopes
. 233
CHAPTER
8.
Л
-Resultants and Chow Polytopes of Toric Varieties
1.
Mixed
(Ль
.,
A*)-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
Л
-determinants
. 329
4.
The proof of the product formula
. 333
Contents
vii
CHAPTER
11.
Regular
A-Determinan
ts and A-Discriminants
1.
Differential forms on a singular toric variety
and the regular
Л
-determinant
.
344
2.
Newton numbers and Newton functions
. 351
3.
The Newton polytope of the regular
A-determinant
and/^-equivalence of
triangulations
. 361
4.
More on D-equivalence
. 370
5.
Relations to real algebraic geometry
. 378
IIL CLASSICAL DISCRIMINANTS AND RESULTANTS
CHAPTER
12.
Discriminants and Resultants for Polynomials in One Variable
1.
An overview of classical formulas and properties
,. 397
2.
Newton poly topes 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. Schläfli's
method
. 475
APPENDIX A. Determinants of Complexes
. 480
APPENDIX B. A. Cayley: On the Theory of Elimination
. 498
Bibliography
. 503
Notes and References
. 513
List of Notations
. 517
Index
. 521 |
| any_adam_object | 1 |
| author | Gelʹfand, Izrailʹ M. 1913-2009 Kapranov, Michail M. 1962- Zelevinskij, Andrej V. |
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| author_sort | Gelʹfand, Izrailʹ M. 1913-2009 |
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| building | Verbundindex |
| bvnumber | BV040111243 |
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| ctrlnum | (OCoLC)796209059 (DE-599)DNB986966371 |
| discipline | Mathematik |
| edition | Reprint of the 1994 ed. |
| format | Book |
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| indexdate | 2024-10-21T06:00:19Z |
| institution | BVB |
| isbn | 9780817647704 |
| language | English |
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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 Reprint of the 1994 ed. Boston [u.a.] Birkhäuser 2008 X, 523 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Modern Birkhäuser classics 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 Erscheint auch als Online-Ausgabe 978-0-8176-4771-1 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024967569&sequence=000002&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 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 | Determinante (DE-588)4138983-9 gnd Resultante (DE-588)4177891-1 gnd Diskriminante (DE-588)4150190-1 gnd |
| topic_facet | Determinante Resultante Diskriminante |
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