Description 
1 online resource (xiv, 268 pages) 
Series 
De Gruyter expositions in mathematics, 09386572 ; 23 

De Gruyter expositions in mathematics ; 23. 09386572

Contents 
""Foreword""; ""Introduction""; ""Basic algorithms in real algebraic geometry and their complexity: from Sturmâ€?s theorem to the existential theory of reals""; ""1. Introduction""; ""2. Real closed fields""; ""2.1. Definition and first examples of real closed fields""; ""2.2. Cauchy index and real root counting""; ""3. Real root counting""; ""3.1. Sylvester sequence""; ""3.2. Subresultants and remainders""; ""3.3. SylvesterHabicht sequence""; ""3.4. Quadratic forms, Hankel matrices and real roots""; ""3.5. Summary and discussion""; ""4. Complexity of algorithms""; ""5. Sign determinations"" 

""2.5. A theorem of Comessatti""""2.6. Group cohomology""; ""2.7. The action of conjugation on the Albanese variety and the Picard group""; ""2.8. Period matrices in pseudonormal form and the Albanese map""; ""3. Real abelian varieties""; ""3.1. Real structures on complex tori""; ""3.2. Equivalence classes for real structures on complex tori""; ""3.3. Line bundles on complex tori with a real structure""; ""3.4. Riemann bilinear relations for principally polarized real varieties""; ""3.5. Moduli spaces of principally polarized real abelian varieties""; ""3.6. Real theta functions"" 

""5.1. Simultaneous inequalities""""5.2. Thomâ€?s lemma and its consequences""; ""6. Existential theory of reals""; ""6.1. Solving multivariate polynomial systems""; ""6.2. Some real algebraic geometry""; ""6.3. Finding points on hypersurfaces""; ""6.4. Finding non empty sign conditions""; ""References""; ""Nash functions and manifolds""; ""Â1. Introduction""; ""Â2. Nash functions""; ""Â3. Approximation Theorem""; ""Â4. Nash manifolds""; ""Â5. Sheaf theory of Nash function germs""; ""Â6. Nash groups""; ""References""; ""Approximation theorems in real analytic and algebraic geometry"" 

""Introduction""""I. The analytic case""; ""1. The Whitney topology for sections of a sheaf""; ""2. A Whitney approximation theorem""; ""3. Approximation for sections of a sheaf""; ""4. Approximation for sheaf homomorphisms""; ""II. The algebraic case""; ""5. Preliminaries on real algebraic varieties""; ""6. A and Bcoherent sheaves""; ""7. The approximation theorems in the algebraic case""; ""III. Algebraic and analytic bundles""; ""8. Duality theory""; ""9. Strongly algebraic vector bundles""; ""10. Approximation for sections of vector bundles""; ""References"" 

""Real abelian varieties and real algebraic curves""""Introduction""; ""1. Generalities on complex tori""; ""1.1. Complex tori""; ""1.2. Homology and cohomology of tori""; ""1.3. Morphisms of complex tori""; ""1.4. The Albanese and the Picard variety""; ""1.5. Line bundles on complex tori""; ""1.6. Polarizations""; ""1.7. Riemannâ€?s bilinear relations and moduli spaces""; ""2. Real structures""; ""2.1. Definition of real structures""; ""2.2. Real models""; ""2.3. The action of conjugation on functions and forms""; ""2.4. The action of conjugation on cohomology"" 
Notes 
"Elaborated versions of the lectures given ... at the Winter School in Real Geometry, held in Universidad Complutense de Madrid, January 37, 1994"Foreword 
Bibliography 
Includes bibliographical references 
Subject 
Geometry, Algebraic.


Geometry, Analytic.

Form 
Electronic book

Author 
Broglia, Fabrizio, 1948

LC no. 
96031731 
ISBN 
3110811111 (electronic bk.) 

9783110811117 (electronic bk.) 
