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Preprints, Working Papers, ... Year : 2021

The Combinatorial PT-DT Correspondence

Abstract

We resolve an open conjecture from algebraic geometry, which states that two generating functions for plane partition-like objects (the "box-counting" formulae for the Calabi-Yau topological vertices in Donaldson-Thomas theory and Pandharipande-Thomas theory) are equal up to a factor of MacMahon's generating function for plane partitions. The main tools in our proof are a Desnanot-Jacobi-type condensation identity, and a novel application of the tripartite double-dimer model of Kenyon-Wilson.

Dates and versions

hal-03115838 , version 1 (19-01-2021)

Identifiers

Cite

Helen Jenne, Gautam Webb, Benjamin Young. The Combinatorial PT-DT Correspondence. 2021. ⟨hal-03115838⟩
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