Stability conditions for generic K3 categories

Details Stability conditions for generic K3 categories Stability conditions for generic K3 categories

2006-08-16

arxiv.org/abs/math/0608430v2

Mathematics

Algebraic Geometry

32 pages, presentation slightly changed, to appear in Compositio Math

Scientific paper

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.

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