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arXiv · 2511.05086

On Universal derivations for multiarrangements

Takuro Abe·Shota Maehara·Gerhard Roehrle·Sven Wiesner
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Abstract

The study of universal derivations for arbitrary multiarrangements and multiplicity functions was initiated by Abe, Röhrle, Stump, and Yoshinaga in 2024 which focused on arrangements arising from (well-generated) reflection groups. In this paper we provide a criterion for determining whether a derivation is universal along with a characterization of universal derivations for arbitrary 2-multiarrangements. As an application we give descriptions of universal derivations for several multiarrangements, including the so-called deleted $A_3$ arrangement. This is the first known example of a non-reflection arrangement that admits a universal derivation distinct from the Euler derivation.

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Takuro Abe, Shota Maehara, Gerhard Roehrle, Sven Wiesner. 2025-11-07. On Universal derivations for multiarrangements. https://arxiv.org/abs/2511.05086

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