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Derived categories of irreducible projective curves of arithmetic genus one

Published online by Cambridge University Press:  25 September 2006

Igor Burban  and
Bernd Kreußler
Igor Burban
Affiliation:
Johannes-Gutenberg Universität Mainz, Fachbereich Physik, Mathematik und Informatik, Institut für Mathematik, 55099 Mainz, Germanyburban@mathematik.uni-mainz.de
Bernd Kreußler
Affiliation:
Mary Immaculate College, South Circular Road, Limerick, Irelandbernd.kreussler@mic.ul.ie
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Abstract

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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.

Keywords

derived categoryelliptic curveFourier–Mukai transformHarder–Narasimhan filtrationstability18E3014H6014H5214H2014H10
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 5 , September 2006 , pp. 1231 - 1262
Copyright
Foundation Compositio Mathematica 2006