Lectures in real geometry:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
de Gruyter
1996
|
| Series: | De Gruyter expositions in mathematics
23 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XIV, 268 S. |
| ISBN: | 3110150956 |
Staff View
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| 245 | 1 | 0 | |a Lectures in real geometry |c ed. Fabrizio Broglia |
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Foreword vii
Stanislaw Lojasiewicz
Introduction ix
MARIE FRANgOISE ROY
Basic algorithms in real algebraic geometry and their complexity:
from Sturm s theorem to the existential theory of reals
1. Introduction 1
2. Real closed fields 4
2.1. Definition and first examples of real closed fields 4
2.2. Cauchy index and real root counting 5
3. Real root counting 6
3.1. Sylvester sequence 7
3.1.1. Definitions and notations 7
3.1.2. Sturm s theorem 8
3.1.3. Computational problems 11
3.2. Subresultants and remainders 12
3.2.1. Definitions 13
3.2.2. Properties of subresultants 14
3.3. Sylvester Habicht sequence 18
3.3.1. Properties of the Sylvester Habicht sequence 18
3.3.2. Sylvester Habicht sequence and Cauchy index 19
3.3.3. Computing the Sylvester Habicht sequence 24
3.4. Quadratic forms, Hankel matrices and real roots 27
3.4.1. Hermite s quadratic form 27
3.4.2. Bezoutians and principal Sylvester Habicht coefficients 31
3.5. Summary and discussion 35
4. Complexity of algorithms 35
5. Sign determinations 38
5.1. Simultaneous inequalities 38
5.1.1. Preliminaries 38
xii Table of Contents
5.1.2. Simultaneous inequalities 40
5.1.3. Complexity of the computation 44
5.2. Thorn s lemma and its consequences 45
5.2.1. Thorn s lemma 45
5.2.2. Coding of real algebraic numbers 46
5.2.3. Sign determination at real algebraic numbers 47
6. Existential theory of reals 48
6.1. Solving multivariate polynomial systems 48
6.1.1. Preliminaries about finite dimensional algebras 48
6.1.2 Univariate Representation Subroutine 53
6.2. Some real algebraic geometry 53
6.3. Finding points on hypersurfaces 55
6.3.1. Preliminaries 55
6.3.2. Cell Representatives Subroutine 58
6.4. Finding non empty sign conditions 60
6.4.1. Preliminaries 61
6.4.2. Sample Points Subroutine 64
References 66
Masahiro Shiota
Nash functions and manifolds
§1. Introduction 69
§2. Nash functions 71
§3. Approximation Theorem 77
§4. Nash manifolds 82
§5. Sheaf theory of Nash function germs 90
§6. Nash groups 100
References 110
Alberto Tognoli
Approximation theorems in real analytic and algebraic geometry
Introduction 113
I. The analytic case 114
1. The Whitney topology for sections of a sheaf 114
Table of Contents xiii
2. A Whitney approximation theorem 118
3. Approximation for sections of a sheaf 126
4. Approximation for sheaf homomorphisms 130
II. The algebraic case 134
5. Preliminaries on real algebraic varieties 134
6. A and B coherent sheaves 139
7. The approximation theorems in the algebraic case 145
III. Algebraic and analytic bundles 148
8. Duality theory 148
9. Strongly algebraic vector bundles 156
10. Approximation for sections of vector bundles 162
References 164
Ciro Ciliberto and Claudio Pedrini
Real abelian varieties and real algebraic curves
Introduction 167
1. Generalities on complex tori 168
1.1. Complex tori 168
1.2. Homology and cohomology of tori 170
1.3. Morphisms of complex tori 171
1.4. The Albanese and the Picard variety 174
1.5. Line bundles on complex tori 176
1.6. Polarizations 177
1.7. Riemann s bilinear relations and moduli spaces 179
2. Real structures 181
2.1. Definition of real structures 182
2.2. Real models 183
2.3. The action of conjugation on functions and forms 185
2.4. The action of conjugation on cohomology 188
2.5. A theorem of Comessatti 191
2.6. Group cohomology 195
2.7. The action of conjugation on the Albanese variety and the Picard group . . 199
2.8. Period matrices in pseudonormal form and the Albanese map 203
xiv Table of Contents
3. Real abelian varieties 206
3.1. Real structures on complex tori 206
3.2. Equivalence classes for real structures on complex tori 211
3.3. Line bundles on complex tori with a real structure 214
3.4. Riemann bilinear relations for principally polarized real varieties 218
3.5. Moduli spaces of principally polarized real abelian varieties 224
3.6. Real theta functions 228
4. Applications to real curves 230
4.1. The Jacobian of a real curve 230
4.2. Real theta characteristics 238
4.3. Examples 244
4.4. Moduli spaces and the theorem of Torelli 248
4.5. Singular curves 251
References 254
Appendix
Alberto Tognoli
Mario Raimondo s contributions to real geometry 257
Tomas Recio and Maria Emilia Alonso
Mario Raimondo s contributions to computer algebra 261
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| discipline | Mathematik |
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| institution | BVB |
| isbn | 3110150956 |
| language | English |
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| physical | XIV, 268 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | de Gruyter |
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| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Lectures in real geometry ed. Fabrizio Broglia Berlin [u.a.] de Gruyter 1996 XIV, 268 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 23 Literaturangaben Géométrie algébrique ram Géométrie analytique ram Geometry, Algebraic Geometry, Analytic Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Analytische Geometrie (DE-588)4001867-2 s DE-604 Algebraische Geometrie (DE-588)4001161-6 s Broglia, Fabrizio Sonstige oth De Gruyter expositions in mathematics 23 (DE-604)BV004069300 23 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007347908&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lectures in real geometry De Gruyter expositions in mathematics Géométrie algébrique ram Géométrie analytique ram Geometry, Algebraic Geometry, Analytic Analytische Geometrie (DE-588)4001867-2 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4001867-2 (DE-588)4001161-6 (DE-588)4143413-4 |
| title | Lectures in real geometry |
| title_auth | Lectures in real geometry |
| title_exact_search | Lectures in real geometry |
| title_full | Lectures in real geometry ed. Fabrizio Broglia |
| title_fullStr | Lectures in real geometry ed. Fabrizio Broglia |
| title_full_unstemmed | Lectures in real geometry ed. Fabrizio Broglia |
| title_short | Lectures in real geometry |
| title_sort | lectures in real geometry |
| topic | Géométrie algébrique ram Géométrie analytique ram Geometry, Algebraic Geometry, Analytic Analytische Geometrie (DE-588)4001867-2 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Géométrie algébrique Géométrie analytique Geometry, Algebraic Geometry, Analytic Analytische Geometrie Algebraische Geometrie Aufsatzsammlung |
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