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. © Springer-Verlag 2009.
CITATION STYLE
Huybrechts, D., & Thomas, R. P. (2009). Deformation-obstruction theory for complexes via Atiyah and Kodaira-Spencer classes. Mathematische Annalen, 346(3), 545–569. https://doi.org/10.1007/s00208-009-0397-6
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