On Universal derivations for multiarrangements
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909892402479104 |
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| author | Abe, Takuro Maehara, Shota Roehrle, Gerhard Wiesner, Sven |
| author_facet | Abe, Takuro Maehara, Shota Roehrle, Gerhard Wiesner, Sven |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05086 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Universal derivations for multiarrangements Abe, Takuro Maehara, Shota Roehrle, Gerhard Wiesner, Sven Combinatorics 52C35, 32S22, 14N20 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. |
| title | On Universal derivations for multiarrangements |
| topic | Combinatorics 52C35, 32S22, 14N20 |
| url | https://arxiv.org/abs/2511.05086 |