# Free and non-free multiplicities on the A3 arrangement

@article{DiPasquale2016FreeAN, title={Free and non-free multiplicities on the A3 arrangement}, author={Michael DiPasquale and Christopher A. Francisco and Jeffrey Mermin and Jay Schweig}, journal={arXiv: Commutative Algebra}, year={2016} }

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.

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