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Stability conditions for derived categories

  • Emanuele Macrì
Chapter
Part of the Progress in Mathematics book series (PM, volume 276)

Abstract

The notion of stability condition on a triangulated category has been introduced by Bridgeland in [65], following ideas from physics by Douglas [104] on π-stability for D-branes. A stability condition on a triangulated category ℑ is given by abstracting the usual properties of μ-stability for sheaves on complex projective varieties; one introduces the notion of slope, using a group homomorphism from the Grothendieck group K(ℑ) of ℑ to ℂ, and requires that a stability condition has generalized Harder-Narasimhan filtrations and is compatible with the shift functor. The main property is that there exists a parameter space Stab(ℑ) for stability conditions, endowed with a natural topology, which is a (possibly infinitedimensional) complex manifold. The space of stability conditions Stab(ℑ) thus yields a geometric invariant naturally attached to a triangulated category ℑ.

Keywords

Stability Condition Modulus Space Stability Function Abelian Category Triangulate Category 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  • Emanuele Macrì
    • 1
  1. 1.University of UtahDepartment of MathematicsSalt Lake CityUT

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