Asymptotic cohomological functions of toric divisors
Algebraic Geometry
2007-06-23 v2
Abstract
We study functions on the class group of a toric variety measuring the rates of growth of the cohomology groups of multiples of divisors. We show that these functions are piecewise polynomial with respect to finite polyhedral chamber decompositions. As applications, we express the self-intersection number of a T-Cartier divisor as a linear combination of the volumes of the bounded regions in the corresponding hyperplane arrangement and prove an asymptotic converse to Serre vanishing.
Cite
@article{arxiv.math/0501104,
title = {Asymptotic cohomological functions of toric divisors},
author = {Milena Hering and Alex Kuronya and Sam Payne},
journal= {arXiv preprint arXiv:math/0501104},
year = {2007}
}
Comments
13 pages. v2: corrected typos, minor revisions. To appear in Adv. Math