On volumes along subvarieties of line bundles with nonnegative Iitaka dimension
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- Gianluca Pacienza (Strasbourg)
- Wednesday 20 January 2010, 14:15-15:15
- MR13, CMS.
If you have a question about this talk, please contact Burt Totaro.
In a joint work with S. Takayama we study the restricted
volume along subvarieties of line bundles with
nonnegative Iitaka
dimension. Our main interest is to compare it with a similar notion defined
in terms of the asymptotic multiplier ideal sheaf, with which it coincides
in the big case. We prove that the former is non-zero if and only if the
latter is. We then study inequalities between them and prove that if they
coincide on every very general curve the line bundle must have zero
Iitaka dimension or be big. In the seminar I will present the
different notions of restricted volume, some of the ideas involved in the
proof and a couple of problems arising from our work.
This talk is part of the Algebraic Geometry Seminar series.
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