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Stability conditions for generic K3 categories

Part of: Abelian categories Surfaces and higher-dimensional varieties (Co)homology theory

Published online by Cambridge University Press:  01 January 2008

Daniel Huybrechts ,
Emanuele Macrì  and
Paolo Stellari
Daniel Huybrechts
Affiliation:
Mathematisches Institut, Universität Bonn, Beringstrasse 1, 53115 Bonn, Germany (email: [email protected])
Emanuele Macrì
Affiliation:
Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany (email: [email protected])
Paolo Stellari
Affiliation:
Dipartimento di Matematica ‘F. Enriques’, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy (email: [email protected])
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Abstract

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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.

Keywords

K3 surfacesderived categoriesstability conditions

MSC classification

Secondary: 18E30: Derived categories, triangulated categories 14J28: $K3$ surfaces and Enriques surfaces 14F22: Brauer groups of schemes
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 1 , January 2008 , pp. 134 - 162
Copyright
Copyright © Foundation Compositio Mathematica 2008