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arXiv · 1711.10341

Multiplicativity of the double ramification cycle

David Holmes·Aaron Pixton·Johannes Schmitt
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Abstract

The double ramification cycle satisfies a basic multiplicative relation DRC(a).DRC(b) = DRC(a).DRC(a + b) over the locus of compact-type curves, but this relation fails in the Chow ring of the moduli space of stable curves. We restore this relation over the moduli space of stable curves by introducing an extension of the double ramification cycle to the small b-Chow ring (the colimit of the Chow rings of all smooth blowups of the moduli space). We use this to give evidence for the conjectured equality between the (twisted) double ramification cycle and a cycle constructed in previous work by the second author.

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David Holmes, Aaron Pixton, Johannes Schmitt. 2017-11-28. Multiplicativity of the double ramification cycle. https://arxiv.org/abs/1711.10341

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