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
DOI: https://doi.org/10.1090/S1056-3911-02-00314-4
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
Email: allcock@math.utexas.edu

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

Domingo Toledo
Affiliation: Department of Mathematics, University of Utah, 155 S 1400 E, Room 233, Salt Lake City, Utah 84112-0090
Email: toledo@math.utah.edu

DOI: https://doi.org/10.1090/S1056-3911-02-00314-4
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 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

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