Free and Non-free Multiplicities on the $A_3$ Arrangement
  We give a complete classification of free and non-free multiplicities on the $A_3$ braid arrangement. Namely, we show that all free multiplicities on $A_3$ 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. 
Michael DiPasquale, Christopher A. Francisco, Jeffrey Mermin, and Jay   Schweig
math.AC