568 research outputs found
T-structures on some local Calabi-Yau varieties
Let be a Fano variety satisfying the condition that the rank of the
Grothendieck group of is one more than the dimension of . Let
denote the total space of the canonical line bundle of , considered as a
non-compact Calabi-Yau variety. We use the theory of exceptional collections to
describe t-structures on the derived category of coherent sheaves on
. The combinatorics of these t-structures is determined by a natural
action of an affine braid group, closely related to the well-known action of
the Artin braid group on the set of exceptional collections on .Comment: 30 page
Stability conditions on triangulated categories
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 -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.Comment: A minor change in terminology (centered slope function becomes
stability function). The result on stability conditions on curves of positive
genus is removed since E. Macri found a much better proof in math/0411613. A
false statement pointed out by S. Okada has also been removed. To appear in
Annals of Math
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