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Derived categories of irreducible projective curves of arithmetic genus one

Igor Burban·Bernd Kreussler
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Abstract

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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Igor Burban, Bernd Kreussler. 2006-02-14. Derived categories of irreducible projective curves of arithmetic genus one. https://arxiv.org/abs/math/0503496

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