Open Collections

Description

An ordered tuple of 1-dimensional subspaces $(L_1, \dots, L_n)$ of a fixed vector space $V$ is a {\em spanning line configuration} if $L_1 + \cdots + L_n = V$. We discuss the combinatorics of spanning line configurations, describing enumerative results when $V$ is a vector space over the finite field $\mathbb{F}_q$, and presenting the cohomology ring of the moduli space of spanning line configurations when $V$ is a vector space over $\mathbb{C}$. We present some ideas about how to extend these results to tuples $(W_1, \dots, W_n)$ of potentially higher-dimensional subspaces $W_i$ of $V$. Joint with Brendan Pawlowski and Andy Wilson.