Normal Functions and the Geometry of Moduli Spaces of Curves

By R. Hain. 2011

129 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/18acd3ffd2f97b6dbbdea138e1f99a853a3f68c2

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Integrals of ψ-classes over double ramification cycles (2012, background): “Hain [4] found the restriction of DRg(a1, .”
THE MODULI SPACE OF TWISTED CANONICAL DIVISORS (2015, methodology): “When restricted to the moduli of curves of compact type, Pg,μ is related to canonical divisors via the Abel–Jacobi map by earlier work of Hain [16].”
The double ramification cycle and the theta divisor (2012, methodology): “ssume that each divisor class appears only once, so we either explicitly state which one we are adding or we sum with symmetric coeﬃcients. This convention is used by Mu¨ller [Mu¨l12] but not by Hain [Hai11]. We use δto denote the divisor classes on the moduli stack and ∆ to denote the divisors on t”