Stability conditions on triangulated categories

Details Stability conditions on triangulated categories Stability conditions on triangulated categories

2002-12-17

arxiv.org/abs/math/0212237v3

Mathematics

Algebraic Geometry

A minor change in terminology (centered slope function becomes stability function). The result on stability conditions on curv

Scientific paper

This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas's notion of $\Pi$-stability. From a mathematical point of view, the most interesting feature of the definition is that the set of stability conditions $\Stab(\T)$ on a fixed category $\T$ has a natural topology, thus defining a new invariant of triangulated categories. After setting up the necessary definitions I prove a deformation result which shows that the space $\Stab(\T)$ with its natural topology is a manifold, possibly infinite-dimensional.

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