Vol. 3, No. 5, 2009

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
Author Index
To Appear
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Other MSP Journals
A general homological Kleiman–Bertini theorem

Susan J. Sierra

Vol. 3 (2009), No. 5, 597–609
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 g G, the sheaf TorjX(g,) vanishes for all j 1. 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.

Keywords
generic transversality, homological transversality, Kleiman's theorem, group action
Mathematical Subject Classification 2000
Primary: 14L30
Secondary: 16S38
Milestones
Received: 9 March 2009
Accepted: 21 July 2009
Published: 9 November 2009
Authors
Susan J. Sierra
Department of Mathematics
University of Washington
Seattle, WA 98195
United States
http://www.math.washington.edu/~sjsierra/