Journal ArticleDOI
The third homology group of the moduli space of curves
About:
This article is published in Duke Mathematical Journal.The article was published on 1991-06-01. It has received 57 citations till now. The article focuses on the topics: Moduli of algebraic curves & Moduli space.read more
Citations
More filters
Book
Moduli of curves
Joe Harris,Ian Morrison +1 more
TL;DR: In this article, the Brill-Noether theory is applied to moduli spaces of curves of curves, and a technique for construction of M_g is described, based on the limit linear series and the Brill noether theory.
Book ChapterDOI
Mapping Class Groups
TL;DR: The mapping class group Mod S of an orientable surface S is defined as the group of isotopy classes of orientation-preserving diffeomorphisms S → S. In addition to being a central object of the topology of surfaces, these groups also play an important role in the theory of Teichmuller spaces and in algebraic geometry as mentioned in this paper.
Journal ArticleDOI
Calculating cohomology groups of moduli spaces of curves via algebraic geometry
TL;DR: The first, second, third, fourth, and fifth rational cohomology groups of the moduli space of stable n-pointed genus g curves, for all g and n, using (mostly) algebro-geometric techniques are given in this article.
Proceedings ArticleDOI
Structure of the mapping class groups of surfaces: a survey and a prospect
TL;DR: In this paper, the authors survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology, and discuss several possible directions for future research.
Mapping class groups and moduli spaces of curves
Richard Hain,Eduard Looijenga +1 more
TL;DR: In this paper, the AMS summer research institute on algebraic geometry at UC Santa Cruz presented a survey paper that also contains some new results, including a survey of the results.
References
More filters
Book ChapterDOI
Towards an Enumerative Geometry of the Moduli Space of Curves
TL;DR: In this paper, a Chow ring for the moduli space M g of curves of genus g and its compactification M g is defined, defining what seem to be the most important classes in this ring and calculating the class of some geometrically important loci in M g in terns of these classes.
Journal ArticleDOI
The Euler characteristic of the moduli space of curves
John Harer,Don Zagier +1 more
TL;DR: In this article, it was shown that the Teichmiiller space can be interpreted as the orbifold Euler characteristic of the moduli space of curves of genus g with base point.
Journal ArticleDOI
The virtual cohomological dimension of the mapping class group of an orientable surface
TL;DR: In this paper, a mapping class group of a surface F of genus g with s punctures and r boundary components was considered and the authors established cohomology properties of F parallel to those of the arithmetic groups.
Journal ArticleDOI
Stability of the homology of the mapping class groups of orientable surfaces
TL;DR: The mapping class group of F = Fgs r is F = rgs = wo(A) where A is the topological group of orientation preserving diffeomorphisms of F which are the identity on dF and fix the s punctures as mentioned in this paper.