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Title Lectures in real geometry / editor Fabrizio Broglia
Published Berlin ; New York : Walter de Gruyter, 1996
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Description 1 online resource (xiv, 268 pages)
Series De Gruyter expositions in mathematics, 0938-6572 ; 23
De Gruyter expositions in mathematics ; 23. 0938-6572
Contents ""Foreword""; ""Introduction""; ""Basic algorithms in real algebraic geometry and their complexity: from Sturm�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. Sylvester-Habicht 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 B-coherent 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. Riemann�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 3-7, 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.)