A Kleiman-Bertini Theorem for sheaf tensor products
Algebraic Geometry
2007-05-23 v4 Commutative Algebra
Abstract
Fix a variety X with a transitive (left) action by an algebraic group G. Let E and F be coherent sheaves on X. We prove that, for elements g in a dense open subset of G, the sheaf Tor_i^X(E, g F) vanishes for all i > 0. When E and F are structure sheaves of smooth subschemes of X in characteristic zero, this follows from the Kleiman-Bertini theorem; our result has no smoothness hypotheses on the supports of E or F, or hypotheses on the characteristic of the ground field.
Cite
@article{arxiv.math/0601202,
title = {A Kleiman-Bertini Theorem for sheaf tensor products},
author = {Ezra Miller and David E Speyer},
journal= {arXiv preprint arXiv:math/0601202},
year = {2007}
}
Comments
5 pages; v2: corrected misspelled title; v3: smoothness of group G added to hypotheses, additional remarks on page 1, slight edit in proof of Lemma 1, to appear in Journal of Algebraic Geometry; v4: corrected omission of the word "dense" from main theorem