Geometry & Topology

Pixton's double ramification cycle relations

Emily Clader and Felix Janda

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1517454115

Digital Object Identifier
doi:10.2140/gt.2018.22.1069

Mathematical Reviews number (MathSciNet)
MR3748684

Zentralblatt MATH identifier
06828604

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

Keywords
moduli of curves tautological ring tautological relations

Citation

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. https://projecteuclid.org/euclid.gt/1517454115


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