English

Compact hyper-K\"ahler categories

Algebraic Geometry 2017-04-11 v3 Category Theory

Abstract

We define and study the notion of hyper-K\"ahler category. On the theoretical side, we focus on construction techniques and deformation theory of such categories. We also study in details some examples : non-commutative Hilbert schemes of points on a K3 surface and a categorical resolution of a relative compactified Prymian constructed by Markushevich and Tikhomirov.

Keywords

Cite

@article{arxiv.1510.04229,
  title  = {Compact hyper-K\"ahler categories},
  author = {Roland Abuaf and Grégoire Menet},
  journal= {arXiv preprint arXiv:1510.04229},
  year   = {2017}
}

Comments

Improved results and two sections of examples have been added with respect to a premiminary version. The last section of examples disproves a conjecture of Kuznetsov. With an appendix by Gr\'egoire Menet

R2 v1 2026-06-22T11:20:27.610Z