UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 27, 2018

939 Evans Hall

3:45PM: Divisors on matroids and their volumes

Christopher Eur

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.

5:00PM: The Excess intersection formula

Ritvik Ramkumar

We will give examples of situations where intersections do not have the expected dimension. We will describe the excess intersection formula which allows us to compute the portion of the intersection that has the expected dimension. Time permitting we will compute the Chow ring of a blowups along smooth subschemes.

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