Free and non-free multiplicities on the A3 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. [ABSTRACT FROM AUTHOR]