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arXiv · 2604.18315

On Coble surfaces and their automorphisms

Federico Pieroni
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Abstract

Given a complex Coble surface $X$ with irreducible boundary $C$, we consider a specific automorphism $T : X \to X$, initially defined by Pompilj. We show that there are two families of Coble surfaces satisfying the condition $T|_C = \mathbb{1}_C$. Every Coble surface $X$ in the first family in nodal, and moreover the stronger equality $T = \mathbb{1}_X$ holds. Meanwhile, the second family is ''small'', since it has codimension $3$ in the moduli space of Coble surfaces.

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Federico Pieroni. 2026-04-20. On Coble surfaces and their automorphisms. https://arxiv.org/abs/2604.18315

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