Divisors on matroids and their volumes
Abstract
The classical volume polynomial in algebraic geometry measures the degrees of ample (and nef) divisors on a smooth projective variety. We introduce an analogous volume polynomial for matroids, and give a complete combinatorial formula. For a realizable matroid, we thus obtain an explicit formula for the classical volume polynomial of the associated wonderful compactification. We then introduce a new invariant called the volume of a matroid as a particular specialization of its volume polynomial, and discuss its algebro-geometric and combinatorial properties in connection to graded linear series on blow-ups of projective spaces.
Cite
@article{arxiv.1803.07103,
title = {Divisors on matroids and their volumes},
author = {Christopher Eur},
journal= {arXiv preprint arXiv:1803.07103},
year = {2019}
}
Comments
23 pages, 3 figures. Revision in the exposition of section 3. Other minor expository improvements. To appear in J. Combin. Theory Ser. A