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Preprints, Working Papers, ... Year : 2023

Hyperbolic geometry and real moduli of five points on the line

Abstract

Let $\mathscr{M}_{\mathbb R}$ be the moduli space of smooth real binary quintics. We show that each connected component of $\mathscr{M}_{\mathbb R}$ is isomorphic to an arithmetic quotient of an open subset of the real hyperbolic plane. Our main result is that the induced metric on $\mathscr{M}_{\mathbb R}$ extends to a complete hyperbolic metric on the moduli space of stable real binary quintics, making it isometric to the hyperbolic triangle of angles $\pi/3$, $\pi/5$ and $\pi/10$.
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Dates and versions

hal-04003092 , version 1 (23-02-2023)

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Olivier de Gaay Fortman. Hyperbolic geometry and real moduli of five points on the line. 2023. ⟨hal-04003092⟩
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