A general homological Kleiman-Bertini theorem

Susan Sierra (University of Michigan)

Monday 14th April, 2008 16:00-17:00 214, Mathematics Building


Let Z and Y be closed subvarieties of a variety X. We say that Z and Y are _homologically_transverse_ if the higher Tor's of their structure sheaves are all 0. Now let G be an algebraic group acting on X. We give conditions on Z that ensure that for any Y, the general translate of Z under the action of G is homologically transverse to Y. This result generalises a recent result of Miller and Speyer for transitive group actions and ultimately goes back to the classical Kleiman-Bertini theorem. We give applications to noncommutative algebraic geometry, including the classification of noncommutative surfaces.

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