Matroid schemes and geometric posets

Abstract: The intersection data of an arrangement of hyperplanes is described by a geometric lattice, or equivalently a simple matroid. There is a rich interplay between this combinatorial structure and the topology of the arrangement complement. In this talk, we will similarly characterize the combinatorial structure underlying certain arrangements of subvarieties by defining a class of geometric posets and a generalization of matroids called matroid schemes. We will discuss some notions from matroid theory which extend to this setting and touch on the topological implications of this framework.

commutative algebraalgebraic geometrycombinatorics

Audience: researchers in the topic

Matroids - Combinatorics, Algebra and Geometry Seminar