English

Normal Functions and the Geometry of Moduli Spaces of Curves

Algebraic Geometry 2013-10-22 v4

Abstract

In this paper normal functions (in the sense of Griffiths) are used to solve and refine geometric questions about moduli spaces of curves. The first application is to a problem posed by Eliashberg: compute the class in the cohomology of M_{g,n}^c of the pullback of the zero section of the universal jacobian along the section that takes [C;x_1,...,x_n] to Sum d_j x_j in Jac (C), where d_1 + ... + d_n = 0. The second application is to slope inequalities of the type discovered by Moriwaki. There is also a discussion of height jumping and its relevance to slope inequalilties.

Keywords

Cite

@article{arxiv.1102.4031,
  title  = {Normal Functions and the Geometry of Moduli Spaces of Curves},
  author = {Richard Hain},
  journal= {arXiv preprint arXiv:1102.4031},
  year   = {2013}
}

Comments

Updated to published version. Also added publication information