| Description |
1 online resource (xiv, 268 pages) |
| Series |
De Gruyter expositions in mathematics, 0938-6572 ; 23 |
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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 |
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5.1. Simultaneous inequalities5.2. 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 |
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IntroductionI. 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 |
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Real abelian varieties and real algebraic curvesIntroduction -- 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 |
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2.5. A theorem of Comessatti2.6. 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 |
| 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 |
| Notes |
English |
| Subject |
Geometry, Analytic.
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Geometry, Algebraic.
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MATHEMATICS -- Geometry -- Algebraic.
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Geometry, Algebraic
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Geometry, Analytic
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| Form |
Electronic book
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| Author |
Broglia, Fabrizio, 1948-
|
| LC no. |
96031731 |
| ISBN |
9783110811117 |
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3110811111 |
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