Compact hyper-Kähler categories

Abstract

We define and study the notion of hyper-Kähler 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.

arXiv commentImproved 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 Grégoire Menet