Strata of discriminantal arrangements

TL;DR

This paper provides an explicit description of the multiplicities of codimension two strata in discriminantal arrangements, explores their connection with Gale transforms, and computes the fundamental groups of their complements.

Contribution

It offers a detailed characterization of strata multiplicities in discriminantal arrangements and links these findings to Gale transforms and fundamental group calculations.

Findings

Explicit description of codimension two strata multiplicities

Connection established between strata properties and Gale transform

Fundamental groups of discriminantal arrangement complements calculated

Abstract

We give an explicit description of the multiplicities of codimension two strata of discriminantal arrangements introduced by Manin and Schechtman. As applications, we discuss the connection of these results with properties of Gale transform and we calculate the fundamental groups of the complements to discriminantal arrangements.