Torelli Groups and Geometry of Moduli Spaces of Curves

Details Torelli Groups and Geometry of Moduli Spaces of Curves Torelli Groups and Geometry of Moduli Spaces of Curves

1994-03-27

arxiv.org/abs/alg-geom/9403015v2

Mathematics

Algebraic Geometry

38 pages, AMS-LaTeX. Abstract of revised version: This is a significanly revised and expanded version of the original paper. S

Scientific paper

In this paper we give an exposition of Dennis Johnson's work on the first homology of the Torelli groups and show how it can be applied, alone and in concert with Saito's theory of Hodge modules, to study the geometry of moduli spaces of curves. For example, we show that the picard groups of moduli spaces of curves with a fixed level structure are finitely generated, classify all "natural" normal functions defined over moduli spaces of curves with a fixed level, and also "compute" the height paring between cycles over moduli spaces of curves which are homologically trivial and disjoint over the generic point. Several new sections have been added. These apply the results on normal functions to prove generalizations of the classical Franchetta conjecture for curves and abelian varieties. In one section, the monodromy group of nth roots of the canonical bundle is computed.

Affiliated with

Also associated with

No associations

Rating

Torelli Groups and Geometry of Moduli Spaces of Curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Torelli Groups and Geometry of Moduli Spaces of Curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Torelli Groups and Geometry of Moduli Spaces of Curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-317442