English

Seiberg-like duality for resolutions of determinantal varieties

Algebraic Geometry 2024-03-11 v1

Abstract

We study the genus-zero Gromov-Witten theory of two natural resolutions of determinantal varieties, termed the PAX and PAXY models. We realize each resolution as lying in a quiver bundle, and show that the respective quiver bundles are related by a quiver mutation. We prove that generating functions of genus-zero Gromov-Witten invariants for the two resolutions are related by a specific cluster change of variables. Along the way, we obtain a quantum Thom-Porteous formula for determinantal varieties and prove a Seiberg-like duality statement for certain quiver bundles.

Keywords

Cite

@article{arxiv.2403.05240,
  title  = {Seiberg-like duality for resolutions of determinantal varieties},
  author = {Nathan Priddis and Mark Shoemaker and Yaoxiong Wen},
  journal= {arXiv preprint arXiv:2403.05240},
  year   = {2024}
}

Comments

38 pages. Comments are welcome!