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.

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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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