UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

October 15, 2013

939 Evans Hall


3:45PM: Closures of a linear space

Adam Boocher

If $L\subset \mathbb{A}^n$ is a linear space then we can take its closure in $(\mathbb{P}^1)^n$ once we fix coordinates. In this talk I'll present joint work with Federico Ardila concerning the defining ideal of the closure. It turns out the combinatorics of this ideal are completely determined by a matroid associated to $L$. We'll compute its degree, universal Gr\"obner basis, and initial ideals - and tell how to read all of this from the matroid. If time permits we will discuss closures of linear spaces inside more general products of projective spaces.

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