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2009 A general homological Kleiman–Bertini theorem
Susan Sierra
Algebra Number Theory 3(5): 597-609 (2009). DOI: 10.2140/ant.2009.3.597

Abstract

Let G be a smooth algebraic group acting on a variety X. Let and be coherent sheaves on X. We show that if all the higher Tor sheaves of against G-orbits vanish, then for generic gG, the sheaf TorjX(g,) vanishes for all j1. 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 Sierra. "A general homological Kleiman–Bertini theorem." Algebra Number Theory 3 (5) 597 - 609, 2009. https://doi.org/10.2140/ant.2009.3.597

Information

Received: 9 March 2009; Accepted: 21 July 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1180.14048
MathSciNet: MR2578891
Digital Object Identifier: 10.2140/ant.2009.3.597

Subjects:
Primary: 14L30
Secondary: 16S38

Keywords: generic transversality , group action , homological transversality , Kleiman's theorem

Rights: Copyright © 2009 Mathematical Sciences Publishers

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Vol.3 • No. 5 • 2009
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