A categorical sl_2 action on some moduli spaces of sheaves
Algebraic Geometry
2023-02-10 v3 Representation Theory
Abstract
We study certain sequences of moduli spaces of sheaves on K3 surfaces, building on work of Markman, Yoshioka, and Nakajima. We show that these sequences can be given the structure of a geometric categorical sl_2 action in the sense of Cautis, Kamnitzer, and Licata. As a corollary, we get an equivalence between derived categories of some moduli spaces that are birational via stratified Mukai flops.
Keywords
Cite
@article{arxiv.2009.08522,
title = {A categorical sl_2 action on some moduli spaces of sheaves},
author = {Nicolas Addington and Ryan Takahashi},
journal= {arXiv preprint arXiv:2009.08522},
year = {2023}
}
Comments
52 pages. v3: reorganized section 9 a little. final version to appear in Trans Amer Math Soc