The moduli space of cubic fourfolds

Details The moduli space of cubic fourfolds The moduli space of cubic fourfolds

2007-04-24

arxiv.org/abs/0704.3256v2

J. Algebraic Geom. 18 (2009), 511-545

Mathematics

Algebraic Geometry

28 pages, part I (the GIT compactification), the journal version

Scientific paper

We describe the GIT compactification of the moduli space of cubic fourfolds,
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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