Multiplicativity of the Double Ramification Cycle
David HolmesMathematisch Instituut, Universiteit Leiden, Postbus 9512 2300 RA, Leiden, Netherlands
Aaron PixtonDepartment of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Johannes SchmittDepartment of Mathematics, ETH Zürich, Raemistrasse 101, 8092 Zürich, Switzerland
The double ramification cycle satisfies a basic multiplicative relation 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 -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 described by the second author in [F. Janda et al., Publ. Math., Inst. Hautes Étud. Sci. 125, 221--266 (2017; Zbl 1370.14029)].
Cite this article
David Holmes, Aaron Pixton, Johannes Schmitt, Multiplicativity of the Double Ramification Cycle. Doc. Math. 24 (2019), pp. 545–562DOI 10.4171/DM/688