Moduli spaces of residueless meromorphic differentials and the KP hierarchy

Abstract

We prove that the cohomology classes of the moduli spaces of residueless meromorphic differentials, i.e., the closures, in the moduli space of stable curves, of the loci of smooth curves whose marked points are the zeros and poles of prescribed orders of a meromorphic differential with vanishing residues, form a partial cohomological field theory (CohFT) of infinite rank. To this partial CohFT we apply the double ramification hierarchy construction to produce a Hamiltonian system of evolutionary PDEs. We prove that its reduction to the case of differentials with exactly two zeros and any number of poles coincides with the KP hierarchy up to a change of variables.

arXiv comment26 pages

References in corpus (12)

• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• Double ramification cycles on the moduli spaces of curves
• Compactification of strata of abelian differentials
• Double ramification cycles and integrable hierarchies
• Integrals of psi-classes over double ramification cycles
• The moduli space of twisted canonical divisors
• Tau-structure for the Double Ramification Hierarchies
• Integrable systems of double ramification type
• Flat F-manifolds, F-CohFTs, and integrable hierarchies
• Cohomology classes of strata of differentials
• Quadratic double ramification integrals and the noncommutative KdV hierarchy
• Integrability, Quantization and Moduli Spaces of Curves