Mathematische Annalen

, 346:545 | Cite as

Deformation-obstruction theory for complexes via Atiyah and Kodaira–Spencer classes

  • Daniel Huybrechts
  • Richard P. Thomas


We give a universal approach to the deformation-obstruction theory of objects of the derived category of coherent sheaves over a smooth projective family. We recover and generalise the obstruction class of Lowen and Lieblich, and prove that it is a product of Atiyah and Kodaira–Spencer classes. This allows us to obtain deformation-invariant virtual cycles on moduli spaces of objects of the derived category on threefolds.


Modulus Space Exact Sequence Simple Complex Coherent Sheave Extension Class 
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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität BonnBonnGermany
  2. 2.Department of MathematicsImperial CollegeLondonUK

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