Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



The complex hyperbolic geometry of the moduli space of cubic surfaces

Authors: Daniel Allcock, James A. Carlson and Domingo Toledo
Journal: J. Algebraic Geom. 11 (2002), 659-724
Published electronically: July 2, 2002
MathSciNet review: 1910264
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Abstract | References | Additional Information

Abstract: We prove that the moduli space of semistable cubic surfaces over the complex numbers is biholomorphic to the Satake compactification of the quotient of the four-ball by the projective unitary group of the standard Hermitian form of signature $(4,1)$ with coefficients in the ring of integers of $\mathbb {Q}(\sqrt {-3})$. We also explain the precise relation between the orbifold structures on the moduli space of stable cubic surfaces and on the quotient of the ball.

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Additional Information

Daniel Allcock
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
MR Author ID: 620316

James A. Carlson
Affiliation: Department of Mathematics, University of Utah, 155 S 1400 E JWB 233, Salt Lake City, Utah 84112-0090

Domingo Toledo
Affiliation: Department of Mathematics, University of Utah, 155 S 1400 E, Room 233, Salt Lake City, Utah 84112-0090

Received by editor(s): July 9, 2000
Received by editor(s) in revised form: February 9, 2001
Published electronically: July 2, 2002
Additional Notes: The first author was partially supported by an NSF postdoctoral fellowship. The second and third authors [1] were partially supported by NSF grants DMS 9625463 and DMS 9900543. The third author was partially supported by the IHES
Dedicated: To Herb Clemens on his 60th birthday