Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group

Fuente: arXiv
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Main Authors: Baldi, Gregorio, Farb, Benson, Javanpeykar, Ariyan, Stover, Matthew
Format: Preprint
Published: 2026
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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