On the Geometry of the Moduli Space of Real Binary Octics

Chu, Kenneth C. K.

Canadian journal of mathematics, Tome 63 (2011) no. 4, pp. 755-797

Résumé

The moduli space of smooth real binary octics has five connected components. They parametrize the real binary octics whose defining equations have 0, ... , 4 complex-conjugate pairs of roots respectively. We show that each of these five components has a real hyperbolic structure in the sense that each is isomorphic as a real-analytic manifold to the quotient of an open dense subset of 5-dimensional real hyperbolic space $\mathbb{R}{{\mathbb{H}}^{5}}$ by the action of an arithmetic subgroup of Isom $\left( \mathbb{R}{{\mathbb{H}}^{5}} \right)$ . These subgroups are commensurable to discrete hyperbolic reflection groups, and the Vinberg diagrams of the latter are computed.

Détail

DOI : 10.4153/CJM-2011-026-1

Mots-clés : 32G13, 32G20, 14D05, 14D20, real binary octics, moduli space, complex hyperbolic geometry, Vinberg algorithm