Moduli spaces of residueless meromorphic differentials and the KP hierarchy

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 res...

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Bibliographic Details
Published inarXiv.org
Main Authors Buryak, Alexandr, Rossi, Paolo, Zvonkine, Dimitri
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.10.2021
Subjects
Field theory
Hamiltonian functions
Homology
Mathematics - Algebraic Geometry
Mathematics - Mathematical Physics
Physics - Mathematical Physics
Poles
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2110.01419