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.
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An erratum to this article is available at http://dx.doi.org/10.1007/s00208-013-0999-x.
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Huybrechts, D., Thomas, R.P. Deformation-obstruction theory for complexes via Atiyah and Kodaira–Spencer classes. Math. Ann. 346, 545–569 (2010). https://doi.org/10.1007/s00208-009-0397-6
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DOI: https://doi.org/10.1007/s00208-009-0397-6