Inducing stability conditions

Details Inducing stability conditions Inducing stability conditions

2007-05-25

arxiv.org/abs/0705.3752v3

Mathematics

Algebraic Geometry

31 pages. Final version to appear in J. Algebraic Geom

Scientific paper

We study stability conditions induced by functors between triangulated categories. Given a finite group acting on a smooth projective variety we prove that the subset of invariant stability conditions embeds as a closed submanifold into the stability manifold of the equivariant derived category. As an application we examine stability conditions on Kummer and Enriques surfaces and we improve the derived version of the Torelli Theorem for the latter surfaces already present in the litterature. We also study the relationship between stability conditions on projective spaces and those on their canonical bundles.

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