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Mathematische Annalen

, 346:545 | Cite as

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

  • Daniel Huybrechts
  • Richard P. Thomas
Article

Abstract

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.

Keywords

Modulus Space Exact Sequence Simple Complex Coherent Sheave Extension Class 
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

© Springer-Verlag 2009

Authors and Affiliations

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

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