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

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

2008-05-22

arxiv.org/abs/0805.3527v1

Math. Ann. 346, 545--569, 2010.

Mathematics

Algebraic Geometry

22 pages

Scientific paper

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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