Volume and Hilbert function of R-divisors
Algebraic Geometry
2015-03-11 v2
Abstract
If D is a big divisor and E is an effective divisor, then vol(D-E)<=vol(D)<=vol(D+E). We discuss when each inequality is an equality. Surprisingly, the answer is that the asymptotic equality vol(D-E)=vol(D) is equivalent to the equality of the Hilbert functions of D-E and D. The analogous result holds when vol(D)=vol(D+E).
Cite
@article{arxiv.1503.02324,
title = {Volume and Hilbert function of R-divisors},
author = {Mihai Fulger and János Kollár and Brian Lehmann},
journal= {arXiv preprint arXiv:1503.02324},
year = {2015}
}
Comments
Comments welcome