Pixton's double ramification cycle relations
Algebraic Geometry
2018-03-16 v3
Abstract
We prove a conjecture of Pixton, namely that his proposed formula for the double ramification cycle on Mbar_{g,n} vanishes in codimension beyond g. This yields a collection of tautological relations in the Chow ring of Mbar_{g,n}. We describe, furthermore, how these relations can be obtained from Pixton's 3-spin relations via localization on the moduli space of stable maps to an orbifold projective line.
Cite
@article{arxiv.1601.02871,
title = {Pixton's double ramification cycle relations},
author = {Emily Clader and Felix Janda},
journal= {arXiv preprint arXiv:1601.02871},
year = {2018}
}
Comments
40 pages. v2: Correction to proof of Lemma 4.2; results of Section 4 assume that exactly one a_i is negative, and the general case is deduced by polynomiality in A. v3: Substantial changes to Section 6 and the Appendix