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arXiv · 0705.0055

A general homological Kleiman-Bertini theorem

Susan J. Sierra
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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.

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Susan J. Sierra. 2009-08-20. A general homological Kleiman-Bertini theorem. https://arxiv.org/abs/0705.0055

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