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SUMMARY:On volumes along subvarieties of line bundles with nonnegative Iit
 aka dimension - Gianluca Pacienza (Strasbourg)
DTSTART:20100120T141500Z
DTEND:20100120T151500Z
UID:TALK21949@talks.cam.ac.uk
CONTACT:Burt Totaro
DESCRIPTION:In a joint work with S. Takayama we study the restricted\nvolu
 me along subvarieties of line bundles with\nnonnegative Iitaka\ndimension.
  Our main interest is to compare it with a similar notion defined\nin term
 s of the asymptotic multiplier ideal sheaf\, with which it coincides\nin t
 he big case. We prove that the former is non-zero if and only if the\nlatt
 er is. We then study inequalities between them and prove that if they\ncoi
 ncide on every very general curve the line bundle must have zero\nIitaka d
 imension or be big. In the seminar I will present the\ndifferent notions o
 f restricted volume\, some of the ideas involved in the\nproof and a coupl
 e of problems arising from our work.
LOCATION:MR13\, CMS
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