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VOL. 69 | 2016 On derived categories of K3 surfaces, symplectic automorphisms and the Conway group
Daniel Huybrechts

Editor(s) Osamu Fujino, Shigeyuki Kondō, Atsushi Moriwaki, Masa-Hiko Saito, Kōta Yoshioka

Abstract

In this note we interpret a recent result of Gaberdiel et al [7] in terms of derived equivalences of K3 surfaces. We prove that there is a natural bijection between subgroups of the Conway group $C\!o_0$ with invariant lattice of rank at least four and groups of symplectic derived equivalences of $\mathrm{D}^{\mathrm{b}}(X)$ of projective K3 surfaces fixing a stability condition.

As an application we prove that every such subgroup $G\subset C\!o_0$ satisfying an additional condition can be realized as a group of symplectic automorphisms of an irreducible symplectic variety deformation equivalent to $\mathrm{Hilb}^n(X)$ of some K3 surface.

Information

Published: 1 January 2016
First available in Project Euclid: 4 October 2018

zbMATH: 1386.14137
MathSciNet: MR3586514

Digital Object Identifier: 10.2969/aspm/06910387

Subjects:
Primary: 14C30, 14J28

Rights: Copyright © 2016 Mathematical Society of Japan

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