English

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

Algebraic Geometry 2013-09-17 v2

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.

Keywords

Cite

@article{arxiv.0805.3527,
  title  = {Deformation-obstruction theory for complexes via Atiyah and Kodaira--Spencer classes},
  author = {D. Huybrechts and R. P. Thomas},
  journal= {arXiv preprint arXiv:0805.3527},
  year   = {2013}
}

Comments

Corrected flatness problem pointed out by F Langholf and P Bousseau. Updated references. 23 pages