Deformations and Fourier-Mukai transforms

Details Deformations and Fourier-Mukai transforms Deformations and Fourier-Mukai transforms

2005-02-28

arxiv.org/abs/math/0502571v3

Mathematics

Algebraic Geometry

To appear in Journal of Differential Geometry

Scientific paper

The aim of this paper is twofold: First we give an explicit construction of
the infinitesimal deformations of the category Coh(X) of coherent sheaves on a
smooth projective variety X. Secondly we show that any Fourier-Mukai transform
$/Phi/colon D^b(X)/to D^b(Y)$ extends to an equivalence between the derived
categories of the deformed Abelian categories.

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