Isotropic subspaces of Orlik-Solomon algebras

TL;DR

This paper provides a combinatorial description of isotropic subspaces in Orlik-Solomon algebras and links these to linear systems on arrangements with specific crossing types.

Contribution

It introduces a new combinatorial characterization of isotropic subspaces in Orlik-Solomon algebras and connects them to linear systems supported on hyperplane arrangements.

Findings

Characterization of isotropic subspaces via intersection lattice decorations

Relation between isotropic subspaces and linear systems on arrangements

Results applicable to arrangements with isolated non-normal crossings

Abstract

We give a combinatorial characterization of isotropic subspaces in the Orlik- Solomon algebra of a hyperplane arrangement in terms of decorations of its intersection lattice. We then use this characterization to prove a result that relates these isotropic subspaces with linear systems supported on the arrangement, for arrangements with isolated non-normal crossings of a particular form.