This paper is devoted to recent progress made towards the understanding of closed bosonic
and fermionic string perturbation theory, formulated in a Lorentz-covariant way on Euclidean …

“Geometric Invariant Theory” by Mumford/Fogarty (the first edition was published in 1965, a
second, enlarged edition appeared in 1982) is the standard reference on applications of …

We define chiral vertex operators and duality matrices and review the fundamental identities
they satisfy. In order to understand the meaning of these equations, and therefore of …

This book offers an easy and compact access to the theory of TeichmA1/4ller spaces,
starting from the most elementary aspects to the most recent developments, eg the role this …

The goal of this book is to give a comprehensive exposition of the relations among the
following three topics: tensor categories (such as a category of representations of a quantum …

The goal of this paper is to formulate and to begin an exploration of the enumerative
geometry of the set of all curves of arbitrary genus g. By this we mean setting up a Chow ring …

Aims Theaimofthisbookistoprovideaguidetoarich…-ject: algebraic curves, and how they vary
in families. The revolution that the? eld of algebraic geometry has undergone with the introd …

Abstract CONTENTS Introduction § 1. Complexes of curves and families of functions § 2.
Singularities and non-degeneracy of functions § 3. Some variants of the complex of curves § …

Let F be the mapping class group of an orientable surface F of genus g with r boundary
components and s punctures. The main theorem of this paper is that for g> 3k-1, Hk (F) is …

Let F= F~ r be the mapping class group of a surface F of genus g with s punctures and r
boundary components. The purpose of this paper is to establish cohomology properties of F …