Algebraic Geometry Seminar
Alex Kueronya
Freiburg
Arithmetic properties of volumes of divisors
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.
Wednesday March 9, 2011 at 4:00 PM in SEO 1227