Espace des modules de certains polyedres projectifs miroirs

Details Espace des modules de certains polyedres projectifs miroirs Espace des modules de certains polyedres projectifs miroirs

2008-06-22

arxiv.org/abs/0806.3569v2

Geometriae Dedicata, 2010, Volume 147, Number 1, Pages 47-86

Mathematics

Geometric Topology

33 pages, 11 figures

Scientific paper

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 $\R^d$, 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.

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