Geometriae Dedicata

, Volume 173, Issue 1, pp 365–392

Quotient categories, stability conditions, and birational geometry

Original Paper


This article deals with the quotient category of the category of coherent sheaves on an irreducible smooth projective variety by the full subcategory of sheaves supported in codimension greater than c. We prove that this category has homological dimension c. As an application, we describe the space of stability conditions on its derived category in the case c \(=\) 1. Moreover, we describe all exact equivalences between these quotient categories in this particular case, which is closely related to classification problems in birational geometry.


Stability conditions Abelian or triangulated quotient categories  Birational maps 

Mathematics Subject Classification


Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Fachbereich C – Mathematik und NaturwissenschaftenBergische Universität WuppertalWuppertalGermany
  2. 2.Mathematisches InstitutHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

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