The moduli space of cubic fourfolds via the period map
By R. Laza. 2007
117 citations recorded by the source corpus.
We characterize the image of the period map for cubic fourfolds with at worst simple singularities as the complement of an arrangement of hyperplanes in the period space. It follows then that the GIT compactification of the moduli space of cubic fourfolds is isomorphic to the Looijenga's compactification associated to this arrangement. This work builds on and is a natural continuation of our previous paper on the GIT compactification of the moduli space of cubic fourfolds.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7b1aa19bc8dd5a0a0d67608acae7cd4727c9f2a3
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In Geometry and Topology
- Alexander Perry
- O. Debarre
- E. Looijenga
- D. Huybrechts
- Laurent Manivel
- Alexander Kuznetsov
- P. Stellari
- Emanuele Macrì
In Mathematical Physics
- Alexander Perry
- O. Debarre
- D. Huybrechts
- Laurent Manivel
- E. Looijenga
- Alexander Kuznetsov
- P. Stellari
- Emanuele Macrì
Citations in the corpus
- The K3 category of a cubic fourfold (2015, background): “1], which is based on Kuznetsov’s work [34] and on the description of the image of the period map for cubic fourfolds due to Laza [41] and Looijenga [45].”
- The period map for cubic fourfolds (2007, methodology): “…19 arithmetic reflection group that we obtained long ago for K3 surfaces of degree 2 and that is described in [10], p. 82ff.) The proof uses in a fundamental way the techniques and results that we developed in [8] and (jointly with Swierstra) in [9], with applications as the present one in mind.”
- Special prime Fano fourfolds of degree 10 and index 2 (2013, background): “orresponds to a point in the period domain C of cubic fourfolds. To make sure that it corresponds to a (then unique) smooth cubic fourfold, we need to check that it is not in the special loci C2 ∪C6 ([La], Theorem 1.1). If the period point of X is general in Dd, the period point in C is general in C”
- The integral Hodge conjecture for two-dimensional Calabi–Yau categories (2020, methodology): “1] uses Laza and Looijenga’s description of the image of the period map for cubic fourfolds [60, 63] to show that X is deformation equivalent within the Hodge locus for v to a cubic fourfold containing a plane.”