Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917502632591360 |
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| author | Baldi, Gregorio Farb, Benson Javanpeykar, Ariyan Stover, Matthew |
| author_facet | Baldi, Gregorio Farb, Benson Javanpeykar, Ariyan Stover, Matthew |
| contents | Let $\mathcal{C}$ be the moduli space of smooth complex cubic surfaces and let $π_1(\mathcal{C})$ be its (orbifold) fundamental group. We prove that the ``divisor subgroup'' of $π_1(\mathcal{C})$ is characteristic. This can be interpreted as saying that the group theory of $π_1(\mathcal{C})$ ``remembers'' the divisor of nodal cubic surfaces. We deduce from this group-theoretic result and some basic complex analysis that $\mathcal{C}$ has no nontrivial biholomorphic automorphisms as complex analytic orbifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16658 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group Baldi, Gregorio Farb, Benson Javanpeykar, Ariyan Stover, Matthew Algebraic Geometry Group Theory Geometric Topology Let $\mathcal{C}$ be the moduli space of smooth complex cubic surfaces and let $π_1(\mathcal{C})$ be its (orbifold) fundamental group. We prove that the ``divisor subgroup'' of $π_1(\mathcal{C})$ is characteristic. This can be interpreted as saying that the group theory of $π_1(\mathcal{C})$ ``remembers'' the divisor of nodal cubic surfaces. We deduce from this group-theoretic result and some basic complex analysis that $\mathcal{C}$ has no nontrivial biholomorphic automorphisms as complex analytic orbifold. |
| title | Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group |
| topic | Algebraic Geometry Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2605.16658 |