Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Divisors on matroids and their volumes

Seminar | February 27 | 3:45-5 p.m. | 939 Evans Hall

 Christopher Eur, UC Berkeley

 Department of Mathematics

The classical volume polynomial in algebraic geometry measures the volumes 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 define an 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.