[Surfaces cubiques réelles et géométrie hyperbolique réelle]
L'espace des modules des surfaces cubiques stables et réelles est le quotient de l'espace hyperbolique réel de dimension quatre par un groupe non-arithmétique discret. Le volume de l'espace des modules est 37π2/1080 dans la métrique de courbure constante −1. Chacune des composantes connexes de l'espace des modules peut être décrite comme le quotient de l'espace hyperbolique réel de dimension quatre par un groupe arithmétique spécifique. Nous calculons le volume des composantes.
The moduli space of stable real cubic surfaces is the quotient of real hyperbolic four-space by a discrete, nonarithmetic group. The volume of the moduli space is 37π2/1080 in the metric of constant curvature −1. Each of the five connected components of the moduli space can be described as the quotient of real hyperbolic four-space by a specific arithmetic group. We compute the volumes of these components.
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@article{CRMATH_2003__337_3_185_0,
author = {Allcock, Daniel and Carlson, James A. and Toledo, Domingo},
title = {Real cubic surfaces and real hyperbolic geometry},
journal = {Comptes Rendus. Math\'ematique},
pages = {185--188},
publisher = {Elsevier},
volume = {337},
number = {3},
year = {2003},
doi = {10.1016/S1631-073X(03)00287-5},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00287-5/}
}
TY - JOUR AU - Allcock, Daniel AU - Carlson, James A. AU - Toledo, Domingo TI - Real cubic surfaces and real hyperbolic geometry JO - Comptes Rendus. Mathématique PY - 2003 SP - 185 EP - 188 VL - 337 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00287-5/ DO - 10.1016/S1631-073X(03)00287-5 LA - en ID - CRMATH_2003__337_3_185_0 ER -
%0 Journal Article %A Allcock, Daniel %A Carlson, James A. %A Toledo, Domingo %T Real cubic surfaces and real hyperbolic geometry %J Comptes Rendus. Mathématique %D 2003 %P 185-188 %V 337 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00287-5/ %R 10.1016/S1631-073X(03)00287-5 %G en %F CRMATH_2003__337_3_185_0
Allcock, Daniel; Carlson, James A.; Toledo, Domingo. Real cubic surfaces and real hyperbolic geometry. Comptes Rendus. Mathématique, Tome 337 (2003) no. 3, pp. 185-188. doi : 10.1016/S1631-073X(03)00287-5. http://www.numdam.org/articles/10.1016/S1631-073X(03)00287-5/
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