Year: 2019
Type: article
Abstract: The double ramification cycle satisfies a basic multiplicative relation \mathrm{DRC}_a \cdot \mathrm{DRC}_b = \mathrm{DRC}_a \cdot \mathrm{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 \mathrm{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 P_g^{d,k}(A) described by the second author in [ F. Janda et al., Publ. Math., Inst. Hautes Étud. Sci. 125, 221–266 (2017; Zbl 1370.14029)].
Source: Documenta Mathematica
DOI: 10.4171/dm/688
Authors: David Holmes, Johannes Schmitt, Aaron Pixton
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2769185081