Alex Kueronya : Arithmetic properties of volumes of divisors

Posted by , part of the Algebraic Geometry Seminar.

At

March 9, 2011, 4 p.m.

In

SEO 1227

Abstract

The volume of a Cartier divisor on an irreducible projective variety describes the asymptotic rate of growth of the number of its global sections. As such, it is a non-negative real number, which happens to be rational whenever the section ring of the divisor in question is finitely generated. In a joint work with Catriona Maclean and Victor Lozovanu we study the multiplicative semigroup of volumes of divisors. We prove that this set is countable on the one hand, on the other hand it contains transcendental elements.