Pixton’s double ramification cycle relations

Clader, Emily; Janda, Felix

doi:10.2140/gt.2018.22.1069

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Pixton's double ramification cycle relations

Emily Clader and Felix Janda

Geometry & Topology 22 (2018) 1069–1108

DOI: 10.2140/gt.2018.22.1069

Abstract

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

Mathematical Subject Classification 2010

Primary: 14H10

Secondary: 14N35

References

Publication

Received: 14 June 2016

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/

Volume 22, issue 2 (2018)