Double-dimer condensation and the PT-DT correspondence
Combinatorics
2022-10-04 v2 Algebraic Geometry
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.
Cite
@article{arxiv.2109.11773,
title = {Double-dimer condensation and the PT-DT correspondence},
author = {Helen Jenne and Gautam Webb and Benjamin Young},
journal= {arXiv preprint arXiv:2109.11773},
year = {2022}
}
Comments
91 pages, 15 figures. This is the full version of the FPSAC extended abstract arXiv:2012.08484