Normal Functions and the Geometry of Moduli Spaces of Curves

Details Normal Functions and the Geometry of Moduli Spaces of Curves Normal Functions and the Geometry of Moduli Spaces of Curves

2011-02-19

arxiv.org/abs/1102.4031v3

Mathematics

Algebraic Geometry

45 pages, major revision: coefficient of d_h^P in Thm. 11.1 (and related results) has been corrected. Thm. 11.5 has been gener

Scientific paper

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.

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