Espace des modules de certains polyèdres projectifs miroirs

Ludovic Marquis (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

A projective mirror polyhedron is a projective polyhedron endowed with reflections across its faces. We construct an explicit diffeomorphism between the moduli space of a mirror projective polyhedron with fixed dihedral angles in $(0,\frac{\pi}{2}]$, and the union of $n$ copies of $\mathbb{R}^d$, when the polyhedron has the combinatorics of an \emph{ecimahedron}, an infinite class of combinatorial polyhedra we introduce here. Moreover, the integers $n$ and $d$ can be computed explicitly in terms of the combinatorics and the fixed dihedral angles.

Domaines: Topologie géométrique [math.GT]

Ludovic Marquis. Espace des modules de certains polyèdres projectifs miroirs. Geometriae Dedicata, 2010, 147 (1), p 47-86. ⟨10.1007/s10711-009-9438-2⟩. ⟨hal-00428904⟩