Derived categories of irreducible projective curves of arithmetic genus one

Details Derived categories of irreducible projective curves of arithmetic genus one Derived categories of irreducible projective curves of arithmetic genus one

2005-03-23

arxiv.org/abs/math/0503496v2

Mathematics

Algebraic Geometry

44 pages; minor modifications; to appear in Compositio Math

Scientific paper

We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all t-structures of this category is given. We describe the moduli space of stability conditions, obtain a complete classification of all spherical objects in this category and show that the group of exact auto-equivalences acts transitively on them. Harder-Narasimhan filtrations in the sense of Bridgeland are used as our main technical tool.

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