Structure of chambers cut out by Veronese arrangements of hyperplanes in the real projective spaces

TL;DR

This paper investigates the geometric structure of chambers formed by specific hyperplane arrangements in real projective spaces, focusing on cases where the number of hyperplanes is three more than the dimension, particularly in three and four dimensions.

Contribution

It provides a detailed analysis of the chamber structures for Veronese arrangements of hyperplanes in real projective spaces, especially for the cases where m=n+3 and n=3 or 4.

Findings

Characterization of chamber structures in specified arrangements

Identification of geometric properties unique to these arrangements

Insights into the combinatorial complexity of hyperplane arrangements

Abstract

We study arrangements of $m$ hyperplanes in the $n$-dimensional real projective space, with a special focus on $m=n+3$ and $n=3$ or $n=4$.