Volume 22, issue 2 (2018)

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Pixton's double ramification cycle relations

Emily Clader and Felix Janda

Geometry & Topology 22 (2018) 1069–1108

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

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moduli of curves, tautological ring, tautological relations
Mathematical Subject Classification 2010
Primary: 14H10
Secondary: 14N35
Received: 14 June 2016
Revised: 20 April 2017
Accepted: 24 May 2017
Published: 16 January 2018
Proposed: Jim Bryan
Seconded: Lothar Göttsche, Richard Thomas
Emily Clader
Department of Mathematics
San Francisco State University
San Francisco, CA
United States
Felix Janda
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States