The moduli space of cubic fourfolds

By R. Laza. 2007

71 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2e51e985686b9a12e942a7a7a8381d70adc4d35a

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In Geometry and Topology

1. E. Looijenga
2. R. Laza
3. Cristiano Spotti
4. Song Sun
5. Alexander Perry
6. Y. Odaka
7. Chi Li
8. G'abor Sz'ekelyhidi

In Mathematical Physics

1. E. Looijenga
2. R. Laza
3. Cristiano Spotti
4. Song Sun
5. Alexander Perry
6. G'abor Sz'ekelyhidi
7. Igor Dolgachev
8. Emanuele Macrì

Citations in the corpus

• The period map for cubic fourfolds (2007, methodology): “The geometric invariant theory for cubic fourfolds has been worked out by Yokoyama [14] (see also Allcock [1]) and more fully by Laza [ 6 ].”
• Explicit Gromov-Hausdorff compactifications of moduli spaces of K\"ahler-Einstein Fano manifolds (2017, background): “GIT of cubic fourfolds has been studied in detail by Laza in [37].”
• The moduli space of cubic fourfolds via the period map (2007, methodology): “The conjugacy classes of subgroups R are easily determined from the results of [27].”