Connectedness and combinatorial interplay in the moduli space of line arrangements
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914689401749504 |
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| author | Guerville-Ballé, Benoît Viu-Sos, Juan |
| author_facet | Guerville-Ballé, Benoît Viu-Sos, Juan |
| contents | This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate combinatorial classes of arrangements whose moduli space is connected. We unify the classes of simple and inductively connected arrangements appearing in the literature. Then, we introduce the notion of arrangements with a rigid pencil form. It ensures the connectedness of the moduli space and is less restrictive that the class of $C_3$ arrangements of simple type. In the last part, we obtain a combinatorial upper bound on the number of connected components of the moduli space. Then, we exhibit examples with an arbitrarily large number of connected components for which this upper bound is sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00322 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Connectedness and combinatorial interplay in the moduli space of line arrangements Guerville-Ballé, Benoît Viu-Sos, Juan Algebraic Geometry Combinatorics 14H10, 14N20, 51A45, 14N10 This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate combinatorial classes of arrangements whose moduli space is connected. We unify the classes of simple and inductively connected arrangements appearing in the literature. Then, we introduce the notion of arrangements with a rigid pencil form. It ensures the connectedness of the moduli space and is less restrictive that the class of $C_3$ arrangements of simple type. In the last part, we obtain a combinatorial upper bound on the number of connected components of the moduli space. Then, we exhibit examples with an arbitrarily large number of connected components for which this upper bound is sharp. |
| title | Connectedness and combinatorial interplay in the moduli space of line arrangements |
| topic | Algebraic Geometry Combinatorics 14H10, 14N20, 51A45, 14N10 |
| url | https://arxiv.org/abs/2309.00322 |