Moduli of Riemann Surfaces, Real Algebraic Curves, and Their Superanalogs

By: S. M. Natanzon

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Hardcover | 1 January 2004

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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. The present book is devoted to the study of topological properties of this space and of similar moduli spaces, such as the space of real algebraic curves, the space of mappings, and also superanalogs of all these spaces. The book can be used by researchers and graduate students working in algebraic geometry, topology, andmathematical physics.

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You Can Find This Book In

Non-Fiction Mathematics Geometry Algebraic Geometry Calculus & Mathematical Analysis Complex Analysis

Introduction	p. 1
Moduli of Riemann Surfaces, Hurwitz Type Spaces and Their Superanalogs	p. 11
Fuchsian groups and their sequential generators	p. 11
The geometry of Fuchsian groups	p. 14
Free Fuchsian groups of rank 2	p. 19
Frike-Klein-Teichmuller type spaces	p. 24
Moduli of Riemann surfaces	p. 29
The space of holomorphic morphisms of Riemann surfaces	p. 31
Lifting Fuchsian groups to SL(2, R)	p. 35
Topological classification of Arf functions and pairs of Arf functions	p. 40
Topological classification of independent Arf functions on compact surfaces	p. 43
The moduli space of spinor framings	p. 46
Super-Fuchsian groups, super-Riemann surfaces and their topological types	p. 48
Moduli of super-Riemann surfaces	p. 50
N = 2 super-Fuchsian groups. N = 2 super-Riemann surfaces and their topological invariants	p. 54
Moduli of N = 2 super-Riemann surfaces	p. 56
Superholomorphic morphisms of super-Riemann surfaces	p. 60
Moduli of Real Algebraic Curves and Their Superanalogs. Differentials, Spinors, and Jacobians of Real Curves	p. 63
Topological types of real algebraic curves	p. 63
Moduli of real algebraic curves	p. 67
Arf functions on real algebraic curves	p. 71
Lifting real Fuchsian groups	p. 75
Spinors of rank 1 on real algebraic curves	p. 79
Holomorphic differentials on real algebraic curves	p. 83
Analogs of Fourier series and the Sturm-Hurwitz theorem on real algebraic curves of arbitrary genus	p. 86
Jacobians and [theta]-functions of real algebraic curves	p. 89
Prymians of real algebraic curves	p. 93
Uniformization of real algebraic curves by Schottky groups	p. 97
Moduli spaces of spinor bundles of rank 1 on real algebraic curves	p. 100
Real algebraic N = 1 supercurves and their moduli space	p. 105
Real algebraic N = 2 supercurves	p. 109
Moduli spaces of real algebraic N = 2 supercurves	p. 112
Spaces of Meromorphic Functions on Complex and Real Algebraic Curves	p. 117
Coverings with simple critical points	p. 117
Coverings with a single degenerate critical value	p. 122
Spaces of complex meromorphic functions	p. 127
Topological structure of real meromorphic functions	p. 131
Connected components of spaces of real meromorphic functions	p. 140
Bibliography	p. 153
Index	p. 159
Table of Contents provided by Rittenhouse. All Rights Reserved.

Moduli of Riemann Surfaces, Real Algebraic Curves, and Their Superanalogs

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