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arXiv · 2506.02512

Extendability of the $B_2$-arrangement

Torsten Hoge·Shota Maehara·Sven Wiesner
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Abstract

Let $(\mathscr{A},m)$ be a free multiarrangement, and let $\mathscr{E}$ be an extension of $(\mathscr{A},m)$. It is well known that if $\mathscr{A}$ is the Coxeter arrangement of type $A_2$, then a free extension of $(\mathscr{A},m)$ always exists. In this work, we demonstrate that if $\mathscr{A}$ is the Coxeter arrangement of type $B_2$, there exist infinitely many multiplicities for which no free extension of $(\mathscr{A},m)$ exists. This result has immediate consequences for the existence of free extensions in higher rank.

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Torsten Hoge, Shota Maehara, Sven Wiesner. 2025-06-03. Extendability of the $B_2$-arrangement. https://arxiv.org/abs/2506.02512

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