Divisors on matroids and their volumes

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:169

Article

关键词: Matroids;    Chow rings;    Volume polynomials;    Wonderful compactifications;    Tropical linear spaces;    Linear series;   

DOI  :  10.1016/j.jcta.2019.105135

来源: Elsevier

【 摘 要 】

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 shifted rank volume of a matroid as a particular specialization of its volume polynomial, and discuss its algebro-geometric and combinatorial properties in connection to linear series on blow-ups of projective spaces. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free