Description
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics.
The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic.
Editorial Board
Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil
Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany
Chapter
3.4. Quadratic forms, Hankel matrices and real roots
pp.：
32 – 41
3.5. Summary and discussion
pp.：
41 – 49
4. Complexity of algorithms
pp.：
49 – 49
5. Sign determinations
pp.：
49 – 52
5.2. Thom’s lemma and its consequences
pp.：
52 – 59
5.1. Simultaneous inequalities
pp.：
52 – 52
6. Existential theory of reals
pp.：
59 – 62
6.2. Some real algebraic geometry
pp.：
62 – 67
6.1. Solving multivariate polynomial systems
pp.：
62 – 62
6.3. Finding points on hypersurfaces
pp.：
67 – 69
6.4. Finding non empty sign conditions
pp.：
69 – 74
Nash functions and manifolds
pp.：
80 – 83
§2. Nash functions
pp.：
83 – 85
§1. Introduction
pp.：
83 – 83
§3. Approximation Theorem
pp.：
85 – 91
§4. Nash manifolds
pp.：
91 – 96
§5. Sheaf theory of Nash function germs
pp.：
96 – 104
§6. Nash groups
pp.：
104 – 114
References
pp.：
114 – 124
Approximation theorems in real analytic and algebraic geometry
pp.：
124 – 127
I. The analytic case
pp.：
127 – 128
Introduction
pp.：
127 – 127
2. A Whitney approximation theorem
pp.：
128 – 132
1. The Whitney topology for sections of a sheaf
pp.：
128 – 128
3. Approximation for sections of a sheaf
pp.：
132 – 140
4. Approximation for sheaf homomorphisms
pp.：
140 – 144
II. The algebraic case
pp.：
144 – 148
5. Preliminaries on real algebraic varieties
pp.：
148 – 148
6. A- and B-coherent sheaves
pp.：
148 – 153
7. The approximation theorems in the algebraic case
pp.：
153 – 159
III. Algebraic and analytic bundles
pp.：
159 – 162
8. Duality theory
pp.：
162 – 162
9. Strongly algebraic vector bundles
pp.：
162 – 170
10. Approximation for sections of vector bundles
pp.：
170 – 176
References
pp.：
176 – 178
Real abelian varieties and real algebraic curves
pp.：
178 – 181
1. Generalities on complex tori
pp.：
181 – 182
Introduction
pp.：
181 – 181
1.1. Complex tori
pp.：
182 – 182
1.2. Homology and cohomology of tori
pp.：
182 – 184
1.3. Morphisms of complex tori
pp.：
184 – 185
1.4. The Albanese and the Picard variety
pp.：
185 – 188
1.5. Line bundles on complex tori
pp.：
188 – 190
1.6. Polarizations
pp.：
190 – 191
1.7. Riemann’s bilinear relations and moduli spaces
pp.：
191 – 193
2. Real structures
pp.：
193 – 195
2.1. Definition of real structures
pp.：
195 – 196
2.2. Real models
pp.：
196 – 197
2.3. The action of conjugation on functions and forms
pp.：
197 – 199
2.4. The action of conjugation on cohomology
pp.：
199 – 202
2.5. A theorem of Comessatti
pp.：
202 – 205
2.6. Group cohomology
pp.：
205 – 209
2.7. The action of conjugation on the Albanese variety and the Picard group
pp.：
209 – 213
2.8. Period matrices in pseudonormal form and the Albanese map
pp.：
213 – 217
3. Real abelian varieties
pp.：
217 – 220
3.1. Real structures on complex tori
pp.：
220 – 220
3.2. Equivalence classes for real structures on complex tori
pp.：
220 – 225
3.3. Line bundles on complex tori with a real structure
pp.：
225 – 228
3.4. Riemann bilinear relations for principally polarized real varieties
pp.：
228 – 232
3.5. Moduli spaces of principally polarized real abelian varieties
pp.：
232 – 238
3.6. Real theta functions
pp.：
238 – 242
4. Applications to real curves
pp.：
242 – 244
4.1. The Jacobian of a real curve
pp.：
244 – 244
4.2. Real theta-characteristics
pp.：
244 – 252
4.3. Examples
pp.：
252 – 258
4.4. Moduli spaces and the theorem of Torelli
pp.：
258 – 262
4.5. Singular curves
pp.：
262 – 265
References
pp.：
265 – 268
Mario Raimondo’s contributions to real geometry
pp.：
271 – 271
Mario Raimondo’s contributions to computer algebra
pp.：
271 – 275
Lectures in Real Geometry
( De Gruyter Expositions in Mathematics )
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