The Pixton class is a nonhomogeneous cohomology class on the moduli space of stable curves M¯¯¯¯¯¯g,n, with nontrivial terms in degree 0,2,4,…,2g, whose top degree part coincides with the double ramification cycle. In this paper, we prove our conjecture from a previous work, claiming that the generating series of intersection numbers of the Pixton class with monomials in the psi-classes gives a solution of the noncommutative KdV hierarchy.
Intersection numbers with Pixton's class and the noncommutative KdV hierarchy.
Paolo Rossi
2024
Abstract
The Pixton class is a nonhomogeneous cohomology class on the moduli space of stable curves M¯¯¯¯¯¯g,n, with nontrivial terms in degree 0,2,4,…,2g, whose top degree part coincides with the double ramification cycle. In this paper, we prove our conjecture from a previous work, claiming that the generating series of intersection numbers of the Pixton class with monomials in the psi-classes gives a solution of the noncommutative KdV hierarchy.
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