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

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.

preprint2013arXivOpen access
D. HuybrechtsR. P. Thomas
math.AG
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D. HuybrechtsR. P. Thomas

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