English

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 A3A_3 braid arrangement. Namely, we show that all free multiplicities on A3A_3 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