Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

The moduli space of cubic fourfolds


Author: Radu Laza
Journal: J. Algebraic Geom. 18 (2009), 511-545
DOI: https://doi.org/10.1090/S1056-3911-08-00506-7
Published electronically: June 5, 2008
MathSciNet review: 2496456
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Abstract | References | Additional Information

Abstract: We describe the GIT compactification of the moduli space of cubic fourfolds (cubic hypersurfaces in the five dimensional projective space), with a special emphasis on the role played by singularities. Our main result is that a cubic fourfold with only isolated simple (A-D-E) singularities is GIT stable. Conversely, with some minor exceptions, the stability for cubic fourfolds is characterized by this condition.


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Additional Information

Radu Laza
Affiliation: Department of Mathematics, University of Michigan, 3863 East Hall, Ann Arbor, Michigan 48109
Email: rlaza@umich.edu

DOI: https://doi.org/10.1090/S1056-3911-08-00506-7
Received by editor(s): March 7, 2007
Received by editor(s) in revised form: October 10, 2007
Published electronically: June 5, 2008

American Mathematical Society