$π_1$ of trigonal loci of strata of abelian differentials
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911201094533120 |
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| author | Lönne, Michael |
| author_facet | Lönne, Michael |
| contents | We investigate locally closed subspaces of projectivized strata of abelian differentials which classify trigonal curves with canonical divisor a multiple of a trigonal divisor. We describe their orbifold structure using linear systems on Segre-Hirzebruch surfaces and obtain results for their orbifold fundamental groups.
Most notable among these orbifolds is the connected component $\mathbf P\mathcal H^{ev}_4(6)$, the projectivisation of the space $\mathcal H^{ev}_4(6)$ of abelian differentials on non-hyperelliptic genus $4$ curves with a single zero of multiplicity 6 providing an even spin structure. Its orbifold fundamental group is identified with the quotient of the Artin group of type $E_8$ by its maximal central subgroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $π_1$ of trigonal loci of strata of abelian differentials Lönne, Michael Algebraic Geometry Geometric Topology 14D05 primary (14F35, 14J27 secondary) We investigate locally closed subspaces of projectivized strata of abelian differentials which classify trigonal curves with canonical divisor a multiple of a trigonal divisor. We describe their orbifold structure using linear systems on Segre-Hirzebruch surfaces and obtain results for their orbifold fundamental groups. Most notable among these orbifolds is the connected component $\mathbf P\mathcal H^{ev}_4(6)$, the projectivisation of the space $\mathcal H^{ev}_4(6)$ of abelian differentials on non-hyperelliptic genus $4$ curves with a single zero of multiplicity 6 providing an even spin structure. Its orbifold fundamental group is identified with the quotient of the Artin group of type $E_8$ by its maximal central subgroup. |
| title | $π_1$ of trigonal loci of strata of abelian differentials |
| topic | Algebraic Geometry Geometric Topology 14D05 primary (14F35, 14J27 secondary) |
| url | https://arxiv.org/abs/2510.06364 |