Cody Roth

Curves Seminar

Monday, March 14th, 2022

Time: 11:00 a.m.  Place: Jeffery Hall Room 222, or Online via Zoom (contact Deepanshu Prasad for Zoom link)

Speaker: Cody Roth

Title: Structure of Orlik Solomon Algebra for Central Arrangements

Abstract: We will show that given any nonempty central arrangement, the $\mathcal{K}$-linear boundary map on $\mathcal{E}$, the exterior algebra formed from the arrangement, can be naturally defined on the corresponding Orlik-Solomon algebra $\mathcal{A}$, and this definition gives an acyclic chain complex $(\mathcal{A}, \partial)$. We also show how $\mathcal{A}$ can be decomposed into a direct sum indexed via the intersection poset of the arrangement.