John Lesieutre : Pathologies of the volume function

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

April 11, 2022, 3 p.m.

In

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Abstract

If L is a line bundle on a variety X, then it is a basic result that h^0(mL) grows roughly polynomially in m. In birational geometry, it is frequently useful to instead fix an ample divisor A and consider the growth of h0(mL+A) as m increases. I will show that the behavior of this growth can be quite strange.