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A Kleiman-Bertini theorem for sheaf tensor products
Author(s):
Ezra
Miller;
David
E
Speyer
Journal:
J. Algebraic Geom.
17
(2008),
335-340.
Posted:
July 2, 2007
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Abstract |
References |
Additional information
Abstract:
Fix a variety  with a transitive (left) action by an algebraic group  . Let  and  be coherent sheaves on  . We prove that for elements  in a dense open subset of  , the sheaf  vanishes for all  . When  and  are structure sheaves of smooth subschemes of  in characteristic zero, this follows from the Kleiman-Bertini theorem; our result has no smoothness hypotheses on the supports of  or  , or hypotheses on the characteristic of the ground field.
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Additional Information:
Ezra
Miller
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota
Email:
ezra@math.umn.edu
David
E
Speyer
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan
Email:
speyer@umich.edu
PII:
S 1056-3911(07)00479-1
Received by editor(s):
March 4, 2006
Received by editor(s) in revised form:
January 30, 2007
Posted:
July 2, 2007
Additional Notes:
The first author gratefully acknowledges support from NSF CAREER award DMS-0449102 and a University of Minnesota McKnight Land-Grant Professorship. The second author is a Clay Research Fellow and is pleased to acknowledge the support of the Clay Mathematics Institute. This paper originated in a visit of David E Speyer to the University of Minnesota, and he is grateful for their excellent hospitality.
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