Moduli spaces of residueless meromorphic differentials and the KP hierarchy

Buryak, Alexandr¹ ; Rossi, Paolo² ; Zvonkine, Dimitri³

¹ Faculty of Mathematics, National Research University Higher School of Economics, Moscow, Russia, Center for Advanced Studies, Skolkovo Institute of Science and Technology, Moscow, Russia, P G Demidov Yaroslavl State University, Yaroslavl, Russia
² Dipartimento di Matematica “Tullio Levi-Civita”, Universita degli Studi di Padova, Padova, Italy
³ Université de Versailles Saint-Quentin-en-Yvelines, CNRS, Versailles, France

Geometry & topology, Tome 28 (2024) no. 6, pp. 2793-2824.

Résumé

We prove that the cohomology classes of the moduli spaces of residueless meromorphic differentials, ie 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.

Détail

DOI : 10.2140/gt.2024.28.2793

Keywords: moduli space of curves, meromorphic differentials, integrable systems, KP hierarchy

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