ENGLISH

The Moduli Space of Curves

By Lucia Caporaso (auth.) , Robbert H. Dijkgraaf , Carel F. Faber , Gerard B. M. van der Geer (eds.)

Book information

Publisher
Birkhäuser Basel
Year
1995
ISBN
978-1-4612-8714-8, 978-1-4612-4264-2
DOI
10.1007/978-1-4612-4264-2
Language
english
Format
PDF
Filesize
42 MB (43610367 bytes)
Series
Progress in Mathematics 129
Edition
1
Pages
563\569
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Topology; Algebraic Topology; Algebraic Geometry

Description

The moduli space Mgof 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. Leading 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. Altogether, this is a lively volume that testifies to the ferment in the field and gives an excellent view of the state of the art for both mathematicians and theoretical physicists. It is a persuasive example of the famous Wignes comment, and its converse, on "the unreasonable effectiveness of mathematics in the natural science." Witteen’s conjecture in 1990 describing the intersection behavior of tautological classes in the cohomology of Mg arose directly from string theory. Shortly thereafter a stunning 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 numerous suggestions for further development. The same problem is given an elegant 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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