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Moduli of Riemann surfaces, real algebraic curves, and their superanalogs

Author: S M Natanzon
Publisher: Providence, R.I. : American Mathematical Society, ©2004.
Series: Translations of mathematical monographs, v. 225.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:

The space of all Riemann surfaces (the so-called moduli space) plays an important role in algebraic geometry and its applications to quantum field theory. This book focuses on the study of  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: S M Natanzon
ISBN: 0821835947 9780821835944
OCLC Number: 55587670
Description: viii, 160 p. : ill. ; 27 cm.
Contents: Chapter 1. Moduli of Riemann Surfaces, Hurwitz Type Spaces and Their Superanalogs 11 --
1. Fuchsian groups and their sequential generators 11 --
2. The geometry of Fuchsian groups 14 --
3. Free Fuchsian groups of rank 2 19 --
4. Frike-Klein-Teichmuller type spaces 24 --
5. Moduli of Riemann surfaces 29 --
6. The space of holomorphic morphisms of Riemann surfaces 31 --
7. Lifting Fuchsian groups to SL(2, R) 35 --
8. Topological classification of Arf functions and pairs of Arf functions 40 --
9. Topological classification of independent Arf functions on compact surfaces 43 --
10. The moduli space of spinor framings 46 --
11. Super-Fuchsian groups, super-Riemann surfaces and their topological types 48 --
12. Moduli of super-Riemann surfaces 50 --
13. N = 2 super-Fuchsian groups. N = 2 super-Riemann surfaces and their topological invariants 54 --
14. Moduli of N = 2 super-Riemann surfaces 56 --
15. Superholomorphic morphisms of super-Riemann surfaces 60 --
Chapter 2. Moduli of Real Algebraic Curves and Their Superanalogs. Differentials, Spinors, and Jacobians of Real Curves 63 --
1. Topological types of real algebraic curves 63 --
2. Moduli of real algebraic curves 67 --
3. Arf functions on real algebraic curves 71 --
4. Lifting real Fuchsian groups 75 --
5. Spinors of rank 1 on real algebraic curves 79 --
6. Holomorphic differentials on real algebraic curves 83 --
7. Analogs of Fourier series and the Sturm-Hurwitz theorem on real algebraic curves of arbitrary genus 86 --
8. Jacobians and [theta]-functions of real algebraic curves 89 --
9. Prymians of real algebraic curves 93 --
10. Uniformization of real algebraic curves by Schottky groups 97 --
11. Moduli spaces of spinor bundles of rank 1 on real algebraic curves 100 --
12. Real algebraic N = 1 supercurves and their moduli space 105 --
13. Real algebraic N = 2 supercurves 109 --
14. Moduli spaces of real algebraic N = 2 supercurves 112 --
Chapter 3. Spaces of Meromorphic Functions on Complex and Real Algebraic Curves 117 --
1. Coverings with simple critical points 117 --
2. Coverings with a single degenerate critical value 122 --
3. Spaces of complex meromorphic functions 127 --
4. Topological structure of real meromorphic functions 131 --
5. Connected components of spaces of real meromorphic functions 140.
Series Title: Translations of mathematical monographs, v. 225.
Other Titles: Moduli rimanovykh poverkhnosteĭ i veshchestvennykh algebraicheskikh krivykh i ikh superanalogi.
Responsibility: S.M. Natanzon ; translated by Sergei Lando.

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