The double ramification cycle and the theta divisor

By S. Grushevsky, D. Zakharov. 2012

54 citations recorded by the source corpus.

We compute the classes of universal theta divisors of degrees zero and g-1 over the Deligne-Mumford compactification of the moduli space of curves, with various integer weights on the points, in particular reproving a recent result of M\"uller. We also obtain a formula for the class in the Chow ring of the moduli space of curves of compact type of the double ramification locus, given by the condition that a fixed linear combination of the marked points is a principal divisor, reproving a recent result of Hain. Our approach for computing the theta divisor is more direct, via test curves and the geometry of the theta divisor, and works easily over the entire Deligne-Mumford compactification. We use our extended result in another paper to study the partial compactification of the double ramification cycle.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/57a9749768848421cdf29857bf12b40896297d0e

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Double ramification cycles on the moduli spaces of curves (2016, methodology): “A simpler approach was later provided by Grushevsky and Zakharov [19].”
Integrals of ψ-classes over double ramification cycles (2012, unknown): “Zakharov [3].”