Nonarithmetic uniformization of some real moduli spaces
type: Item
instance of: scholarly article
title: Nonarithmetic uniformization of some real moduli spaces
zbMATH Open document ID: 1122.14039
author: Daniel Allcock
author: James A. Carlson
author: Domingo Toledo
published in: Geometriae Dedicata
publication date: 2007-05-18T00:00:00Z
review text: In a previous paper [C. R. Math. Acad. Sci., Paris 337, No. 3, 185--188 (2003; Zbl 1055.14057)], the authors described the moduli space of stable real cubic surfaces as a quotient of a real hyperbolic space by a discrete non-arithmetic group. In the present paper, the authors give a more affordable example of a real moduli space which is homeomorphic to a real hyperbolic space modulo a non-arithmetic group. The example is built from the moduli space of stable real polynomials in two variables homogeneous of degree 6. The non-arithmeticity is proved in the spirit of \textit{M. Gromov} and \textit{I. I. Piatetski-Shapiro} [Publ. Math., Inst. Hautes Étud. Sci. 66, 93--103 (1988; Zbl 0649.22007)].
reviewed by: Frédéric Mangolte
Mathematics Subject Classification ID: 14P25
Mathematics Subject Classification ID: 20H15
zbMATH DE Number: 5154825
zbMATH Keywords: moduli spaces
zbMATH Keywords: discrete groups
zbMATH Keywords: hyperbolic geometry
MaRDI profile type: Publication
full work available at URL: s10711-005-9039-7
OpenAlex ID: W2060594444
cites work: The complex hyperbolic geometry of the moduli space of cubic surfaces
cites work: Real cubic surfaces and real hyperbolic geometry
cites work: Monodromy of hypergeometric functions and non-lattice integral monodromy
cites work: Non-arithmetic groups in Lobachevsky spaces
cites work: Generalized Picard lattices arising from half-integral conditions
cites work: Un résultat sur la monodromie. (A result on the monodromy)
cites work: Q4231188
cites work: Q5550846
cites work: Q4075528
DOI: 10.1007/S10711-005-9039-7
description: scientific article; zbMATH DE number 5154825