The Combinatorial PT-DT Correspondence
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Date
2021-11-23
Authors
Webb, Gautam
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
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.
Description
Keywords
Desnanot-Jacobi identity, Donaldson-Thomas theory, double-dimer model, Pandharipande-Thomas theory, plane partitions