A general homological Kleiman-Bertini theorem
Algebraic Geometry
2009-08-21 v4 Rings and Algebras
Abstract
Let G be a smooth algebraic group acting on a variety X. Let F and E be coherent sheaves on X. We show that if all the higher Tor sheaves of F against G-orbits vanish, then for generic g in G, the sheaf Tor^X_j(gF, E) vanishes for all j >0. This generalizes a result of Miller and Speyer for transitive group actions and a result of Speiser, itself generalizing the classical Kleiman-Bertini theorem, on generic transversality, under a general group action, of smooth subvarieties over an algebraically closed field of characteristic 0.
Cite
@article{arxiv.0705.0055,
title = {A general homological Kleiman-Bertini theorem},
author = {Susan J. Sierra},
journal= {arXiv preprint arXiv:0705.0055},
year = {2009}
}