Fourier Mukai Transforms for Gorenstein Schemes

Details Fourier Mukai Transforms for Gorenstein Schemes Fourier Mukai Transforms for Gorenstein Schemes

2005-06-29

arxiv.org/abs/math/0506593v3

Mathematics

Algebraic Geometry

Final version. To appear in Advances in Mathematics

Scientific paper

We extend to singular schemes with Gorenstein singularities or fibered in schemes of that kind Bondal and Orlov's criterion for an integral functor to be fully faithful. We also contemplate a criterion for equivalence. We offer a proof that is new even if we restrict to the smooth case. In addition, we prove that for locally projective Gorenstein morphisms, a relative integral functor is fully faithful if and only if its restriction to each fibre also is it. These results imply the invertibility of the usual relative Fourier-Mukai transform for an elliptic fibration as a direct corollary.

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