Back to Commutative Algebra Seminar: Spring 2018
Commutative Algebra Seminar
Date: Friday, Apr 20, 2018
Time: 2:30PM - 3:20PM
Location: LCB 222
Christopher Eur
University of California, Berkeley
Title |
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. |
Commutative Algebra