Journal of Algebraic Geometry

Author(s): Radu Laza
Journal: J. Algebraic Geom. 18 (2009), 511-545.
Posted: June 5, 2008
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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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