
Lectures in Real Geometry
Description
Alles über E-Books | Antworten auf Fragen rund um E-Books, Kopierschutz und Dateiformate finden Sie in unserem Info- & Hilfebereich.
More details
Other editions
Additional editions


Content
- Intro
- 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
- 5.1. Simultaneous inequalities
- 5.2. Thom'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
- §1. Introduction
- §2. Nash functions
- §3. Approximation Theorem
- §4. Nash manifolds
- §5. Sheaf theory of Nash function germs
- §6. 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
- 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
- 4. Applications to real curves
- 4.1. The Jacobian of a real curve
- 4.2. Real theta-characteristics
- 4.3. Examples
- 4.4. Moduli spaces and the theorem of Torelli
- 4.5. Singular curves
- References
- Appendix
- Mario Raimondo's contributions to real geometry
- Mario Raimondo's contributions to computer algebra
System requirements
File format: PDF
Copy protection: Watermark-DRM (Digital Rights Management)
System requirements:
- Computer (Windows; MacOS X; Linux): Use the free software Adobe Reader, Adobe Digital Editions, or any other PDF viewer of your choice (see eBook Help).
- Tablet/Smartphone (Android; iOS): Install the free app Adobe Digital Editions or another reading app for eBooks, e.g., PocketBook (see eBook Help).
- E-reader: Bookeen, Kobo, Pocketbook, Sony, Tolino and many more (only limited: Kindle).
The file format PDF always displays a book page identically on any hardware. This makes PDF suitable for complex layouts such as those used in textbooks and reference books (images, tables, columns, footnotes). Unfortunately, on the small screens of e-readers or smartphones, PDFs are rather annoying, requiring too much scrolling.
This eBook uses Watermark-DRM, a „soft” copy protection. This means that there are no technical restrictions to prevent illegal distribution. However, there is a personalised watermark embedded in the eBook that can be used to identify the purchaser of the eBook in the event of misuse and to provide evidence for legal purposes.
For more information, see our eBook Help page.