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

@article{Huybrechts2008DeformationobstructionTF,
  title={Deformation-obstruction theory for complexes via Atiyah and Kodaira–Spencer classes},
  author={D. Huybrechts and Richard P. Thomas},
  journal={Mathematische Annalen},
  year={2008},
  volume={346},
  pages={545-569}
}
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. 
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