Elliptic arrangements of complex multiplication type
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911674650329088 |
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| author | Moci, Luca Pagaria, Roberto Pismataro, Maddalena Vargas, Alejandro |
| author_facet | Moci, Luca Pagaria, Roberto Pismataro, Maddalena Vargas, Alejandro |
| contents | We provide a natural definition of an elliptic arrangement, extending the classical framework to an elliptic curve E with complex multiplication. We analyse the intersections of elements of the arrangement and their connected components as End(E)-modules. Furthermore, we prove that the combinatorial data of elliptic arrangements define both an arithmetic matroid and a matroid over the ring End(E). In this way, we obtain a class of arithmetic matroids that is different from the class of arithmetic matroids realizable via toric arrangements. Finally, we show that the Euler characteristic of the complement is an evaluation of the arithmetic Tutte polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19638 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elliptic arrangements of complex multiplication type Moci, Luca Pagaria, Roberto Pismataro, Maddalena Vargas, Alejandro Combinatorics Algebraic Topology 52C35, 14N20 We provide a natural definition of an elliptic arrangement, extending the classical framework to an elliptic curve E with complex multiplication. We analyse the intersections of elements of the arrangement and their connected components as End(E)-modules. Furthermore, we prove that the combinatorial data of elliptic arrangements define both an arithmetic matroid and a matroid over the ring End(E). In this way, we obtain a class of arithmetic matroids that is different from the class of arithmetic matroids realizable via toric arrangements. Finally, we show that the Euler characteristic of the complement is an evaluation of the arithmetic Tutte polynomial. |
| title | Elliptic arrangements of complex multiplication type |
| topic | Combinatorics Algebraic Topology 52C35, 14N20 |
| url | https://arxiv.org/abs/2506.19638 |