Formal deformations and their categorical general fibre
Abstract
We study the general fibre of a formal deformation over the formal disk of a projective variety from the view point of abelian and derived categories. The abelian category of coherent sheaves of the general fibre is constructed directly from the formal deformation and is shown to be linear over the field of Laurent series. The various candidates for the derived category of the general fibre are compared. If the variety is a surface with trivial canonical bundle, we show that the derived category of the general fibre is again a linear triangulated category with a Serre functor given by the square of the shift functor.
Keywords
Cite
@article{arxiv.0809.3201,
title = {Formal deformations and their categorical general fibre},
author = {Daniel Huybrechts and Emanuele Macri and Paolo Stellari},
journal= {arXiv preprint arXiv:0809.3201},
year = {2009}
}
Comments
This paper contains the more formal aspects discussed in the first sections of arXiv:0710.1645v2 which is now split into two independent papers. 23 pages. Final version to appear in Comment. Math. Helv