2025/06/03 by Hoge, Torsten, Maehara, Shota, Wiesner, Sven
#32S22 #51F15 #52C35 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2506.02512
Let (\mathscrA,m) be a free multiarrangement, and let \mathscrE be an extension of (\mathscrA,m). It is well known that if \mathscrA is the Coxeter arrangement of type A2, then a free extension of (\mathscrA,m) always exists. In this work, we demonstrate that if \mathscrA is the Coxeter arrangement of type B2, there exist infinitely many multiplicities for which no free extension of (\mathscrA,m) exists. This result has immediate consequences for the existence of free extensions in higher rank.