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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

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