Alex Stathis : Volume of Line Bundles: measuring how much space big things take up

Posted by Seckin Adali , part of the Graduate Algebraic Geometry Seminar.

At

Jan. 21, 2015, 3 p.m.

In

SEO 712

Abstract

The volume of a line bundle on a smooth projective variety is an asymptotic birational invariant which is closely related to classical birational invariants. We’ll define and discuss the volume following the exposition of Ein, Lazarsfeld, Mustata, Nakayame, and Popa in “Asymptotic Invariants of Line Bundles” (ELMNP). I’ll attempt to fill in the details left out by ELMNP and work some examples fully. An alternative reference is Lazarsfeld’s “Positivity in Algebraic Geometry: Volume 1”.