Geometry & Topology

Pixton's double ramification cycle relations

Emily Clader and Felix Janda

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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.

Article information

Geom. Topol., Volume 22, Number 2 (2018), 1069-1108.

Received: 14 June 2016
Revised: 20 April 2017
Accepted: 24 May 2017
First available in Project Euclid: 1 February 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic)
Secondary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]

moduli of curves tautological ring tautological relations


Clader, Emily; Janda, Felix. Pixton's double ramification cycle relations. Geom. Topol. 22 (2018), no. 2, 1069--1108. doi:10.2140/gt.2018.22.1069.

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