Compositio Mathematica

Research Article

Stability conditions for generic K3 categories

Daniel Huybrechtsa1, Emanuele Macrìa2 and Paolo Stellaria3

a1 Mathematisches Institut, Universität Bonn, Beringstrasse 1, 53115 Bonn, Germany (email: huybrech@math.uni-bonn.de)

a2 Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany (email: macri@mpim-bonn.mpg.de)

a3 Dipartimento di Matematica ‘F. Enriques’, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy (email: paolo.stellari@mat.unimi.it)

Abstract

A K3 category is by definition a Calabi–Yau category of dimension two. Geometrically K3 categories occur as bounded derived categories of (twisted) coherent sheaves on K3 or abelian surfaces. A K3 category is generic if there are no spherical objects (or just one up to shift). We study stability conditions on K3 categories as introduced by Bridgeland and prove his conjecture about the topology of the stability manifold and the autoequivalences group for generic twisted projective K3, abelian surfaces, and K3 surfaces with trivial Picard group.

(Received November 08 2006)

(Accepted March 26 2007)

(Online publication January 23 2008)

Keywords

  • K3 surfaces;
  • derived categories;
  • stability conditions

2000 Mathematics subject classification

  • 18E30;
  • 14J28;
  • 14F22