The Moduli space of curves
著者
書誌事項
The Moduli space of curves
（Progress in mathematics, v. 129）
Birkhäuser, c1995
- : us
- : sz
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注記
"The conference The Moduli Space of Curves, Texel '94, which was held on Texel Island during the last week of April 1994"--P. vii
Includes bibliographical references
内容説明・目次
- 巻冊次
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: us ISBN 9780817637842
内容説明
The moduli space Mg of curves of fixed genus g - that is, the algebraic variety that parametrizes all curves of genus g - is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.
目次
Distribution of rational points and Kodaira dimension of fiber products.- How many rational points can a curve have?.- Quantum cohomology of rational surfaces.- Quantum intersection rings.- Mirror symmetry and elliptic curves.- A generalized Jacobi theta function and quasimodular forms.- Boundary behaviour of Hurwitz schemes.- Operads and moduli spaces of genus 0 Riemann surfaces.- Resolution of diagonals and moduli spaces.- The Chow ring of the moduli space of curves of genus 5.- The cohomology of algebras over moduli spaces.- Enumeration of rational curves via torus actions.- Cellular decompositions of compactified moduli spaces of pointed curves.- Generating functions in algebraic geometry and sums over trees.- Holomorphicity and non-holomorphicity in N = 2 supersymmetric field theories.- An arithmetic problem in surface geometry.- An orbifold partition of
$$
\bar M_g^n
$$.- Moduli of curves with non-abelian level structure.- Q-structure of conformal field theory with gauge symmetries.- On the cohomology of moduli spaces of rank two vector bundles over curves.
- 巻冊次
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: sz ISBN 9783764337841
内容説明
Developments in theoretical physics, in particular in conformal field theory, have led to a surprising connection to algebraic geometry, and especially to the fundamental concept of the moduli space Mg of curves of genus g, which is the variety that parametrizes all curves of genus g. Experts in the field explore in this volume both the structure of the moduli space of curves and its relationship with physics through quantum cohomology. Witten's conjecture in 1990 describing the intersection behaviour of tautological classes in the cohomology of Mg arose directly from string theory. Shortly thereafter an interesting proof was provided by Kontsevich who, in this volume, describes his solution to the problem of counting rational curves on certain algebraic varieties and includes suggestions for further development. The same problem is given treatment in a paper by Manin. There follows a number of contributions to the geometry, cohomology and arithmetic of the moduli spaces of curves. In addition, several contributors address quantum cohomology and conformal field theory.
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