The double ramification cycle and the theta divisor

Samuel Grushevsky, Dmitry Zakharov

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20 Scopus citations

Abstract

We compute the classes of universal theta divisors of degrees zero and g−1 over the Deligne-Mumford compactification Mg,n of the moduli space of curves, with various integer weights on the points, in particular reproving a recent result of Müller. We also obtain a formula for the class in CHg (Mctg,n) (moduli of stable curves of compact type) of the double ramification cycle, 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 all of Mg,n. We used our extended result in another paper to study the partial compactification of the double ramification cycle.

Original languageEnglish
Pages (from-to)4053-4064
Number of pages12
JournalProceedings of the American Mathematical Society
Volume142
Issue number12
DOIs
StatePublished - 2014

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