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G'eom'etrie alg'ebrique/Algebraic geometry A Complex Hyperbolic Structure for Moduli of Cubic Surfaces
 

Summary: G'eom'etrie alg'ebrique/Algebraic geometry
A Complex Hyperbolic Structure for Moduli of Cubic Surfaces
Daniel Allcock, James A. Carlson, and Domingo Toledo
Department of Mathematics
University of Utah
Salt Lake City, Utah, USA.
E­mail: allcock, carlson and toledo at math.utah.edu
Abstract. We show that the moduli space M of marked cubic surfaces is biholomorphic
to (B 4 \Gamma H)=\Gamma 0
where B 4 is complex hyperbolic four­space, where \Gamma 0
is a specific group
generated by complex reflections, and where H is the union of reflection hyperplanes for
\Gamma 0
. Thus M has complex hyperbolic structure, i.e., an (incomplete) metric of constant
holomorphic sectional curvature.
Une structure hyperbolique complexe pour les modules des surfaces cubiques
R'esum'e. Nous montrons que l''espace des modules M des surfaces cubiques marqu'ees
est biholomorphe `a (B 4 \Gamma H)=\Gamma 0
o'u B 4 est l''espace complexe hyperbolique de dimenson
quatre, o'u \Gamma 0

  

Source: Allcock, Daniel - Department of Mathematics, University of Texas at Austin

 

Collections: Mathematics