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 $\pi/10$.
Domains
Algebraic Geometry [math.AG]
Origin : Files produced by the author(s)