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arXiv · 2605.16658

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

Gregorio Baldi·Benson Farb·Ariyan Javanpeykar·Matthew Stover
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Abstract

Let $\mathcal{C}$ be the moduli space of smooth complex cubic surfaces and let $\pi_1(\mathcal{C})$ be its (orbifold) fundamental group. We prove that the ``divisor subgroup'' of $\pi_1(\mathcal{C})$ is characteristic. This can be interpreted as saying that the group theory of $\pi_1(\mathcal{C})$ ``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.

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Gregorio Baldi, Benson Farb, Ariyan Javanpeykar, Matthew Stover. 2026-05-15. Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group. https://arxiv.org/abs/2605.16658

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