Volume 22, issue 2 (2018)

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Pixton's double ramification cycle relations

Geometry & Topology 22 (2018) 1069–1108
Abstract

We prove a conjecture of Pixton, namely that his proposed formula for the double ramification cycle on ${\stackrel{̄}{M}}_{g,n}$ vanishes in codimension beyond $g$. This yields a collection of tautological relations in the Chow ring of ${\stackrel{̄}{M}}_{g,n}$. 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.

Keywords
moduli of curves, tautological ring, tautological relations
Primary: 14H10
Secondary: 14N35
Publication
Revised: 20 April 2017
Accepted: 24 May 2017
Published: 16 January 2018
Proposed: Jim Bryan
Seconded: Lothar Göttsche, Richard Thomas
Authors
 Emily Clader Department of Mathematics San Francisco State University San Francisco, CA United States https://sites.google.com/site/emilyclader/ Felix Janda Department of Mathematics University of Michigan Ann Arbor, MI United States http://www-personal.umich.edu/~janda/