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Geometry of Algebraic Curves: Volume II with a contribution by Joseph Daniel Harris / Edition 1
     

Geometry of Algebraic Curves: Volume II with a contribution by Joseph Daniel Harris / Edition 1

by Enrico Arbarello, Joseph Daniel Harris, Maurizio Cornalba, Phillip Griffiths
 

ISBN-10: 3540426884

ISBN-13: 9783540426882

Pub. Date: 04/29/2011

Publisher: Springer Berlin Heidelberg

The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface

Overview

The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source.

The first volume appeared 1985 as vol. 267 of the same series.

Product Details

ISBN-13:
9783540426882
Publisher:
Springer Berlin Heidelberg
Publication date:
04/29/2011
Series:
Grundlehren der mathematischen Wissenschaften Series , #268
Edition description:
2011
Pages:
963
Product dimensions:
6.40(w) x 9.30(h) x 1.90(d)

Table of Contents

Preface.- Guide to the Reader.- Chapter IX. The Hilbert Scheme.- Chapter X. Nodal curves.- Chapter XI. Elementary deformation theory and some applications.- Chapter XII. The moduli space of stable curves.- Chapter XIII. Line bundles on moduli.- Chapter XIV. The projectivity of the moduli space of stable curves.- Chapter XV. The Teichmüller point of view.- Chapter XVI. Smooth Galois covers of moduli spaces.- Chapter XVII. Cycles on the moduli spaces of stable curves.- Chapter XVIII. Cellular decomposition of moduli spaces.- Chapter XIX. First consequences of the cellular decomposition .- Chapter XX. Intersection theory of tautological classes.- Chapter XXI. Brill-Noether theory on a moving curve.- Bibliography.- Index.

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