Free and Non-free Multiplicities on the $A_3$ Arrangement
Commutative Algebra
2016-09-02 v1
Abstract
We give a complete classification of free and non-free multiplicities on the braid arrangement. Namely, we show that all free multiplicities on fall into two families that have been identified by Abe-Terao-Wakefield (2007) and Abe-Nuida-Numata (2009). The main tool is a new homological obstruction to freeness derived via a connection to multivariate spline theory.
Keywords
Cite
@article{arxiv.1609.00337,
title = {Free and Non-free Multiplicities on the $A_3$ Arrangement},
author = {Michael DiPasquale and Christopher A. Francisco and Jeffrey Mermin and Jay Schweig},
journal= {arXiv preprint arXiv:1609.00337},
year = {2016}
}
Comments
27 pages, 2 tables, 5 figures