On the Jordan–Hölder property for geometric derived categories

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Autor/in:
Erscheinungsjahr:
2014
Medientyp:
Text
Schlagworte:
  • Derived categories
  • Semiorthogonal decompositions
  • Exceptional objects
  • Jordan–Hölder property
  • Godeaux surface
Beschreibung:
  • We prove that the semiorthogonal decompositions of the derived category of the classical Godeaux surface X do not satisfy the Jordan-Hölder property. More precisely, there are two maximal exceptional sequences in this category, one of length 11, the other of length 9. Assuming the Noetherian property for semiorthogonal decompositions, one can define, following Kuznetsov, the Clemens-Griffiths component CG(D) for each fixed maximal decomposition D. We then show that Db(X) has two different maximal decompositions for which the Clemens-Griffiths components differ. Moreover, we produce examples of rational fourfolds whose derived categories also violate the Jordan-Hölder property. © 2014 Elsevier Inc.
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  • info:eu-repo/semantics/restrictedAccess
Quellsystem:
Forschungsinformationssystem der UHH
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oai:www.edit.fis.uni-hamburg.de:publications/7735e7dc-e7db-4e27-b725-e98c3a182d88