The combinatorial PT-DT correspondence
Combinatorics
2020-12-21 v1 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.2012.08484,
title = {The combinatorial PT-DT correspondence},
author = {Helen Jenne and Gautam Webb and Benjamin Young},
journal= {arXiv preprint arXiv:2012.08484},
year = {2020}
}
Comments
This is an extended abstract submitted to FPSAC 2021