Pixton’s double ramification cycle relations

Clader, Emily¹ ; Janda, Felix²

¹ Department of Mathematics, San Francisco State University, San Francisco, CA, United States
² Department of Mathematics, University of Michigan, Ann Arbor, MI, United States

Geometry & topology, Tome 22 (2018) no. 2, pp. 1069-1108.

Résumé

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.

Détail

DOI : 10.2140/gt.2018.22.1069

Classification : 14H10, 14N35
Keywords: moduli of curves, tautological ring, tautological relations

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