Fourier Mukai Transforms for Gorenstein Schemes
代数几何
2007-05-23 v3 交换代数
摘要
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.
引用
@article{arxiv.math/0506593,
title = {Fourier Mukai Transforms for Gorenstein Schemes},
author = {D. Hernandez Ruiperez and A. C. Lopez Martin and F. Sancho de Salas},
journal= {arXiv preprint arXiv:math/0506593},
year = {2007}
}
备注
Final version. To appear in Advances in Mathematics