Special prime Fano fourfolds of degree 10 and index 2
By O. Debarre, A. Iliev, Laurent Manivel. 2013
59 citations recorded by the source corpus.
Mukai proved that most prime Fano fourfolds of degree 10 and index 2 are contained in a Grassmannian G(2,5). They are all unirational and some are rational, as remarked by Roth in 1949. We show that their middle cohomology is of K3 type and that their period map is dominant, with smooth 4-dimensional fibers, onto a 20-dimensional bounded symmetric period domain of type IV. Following Hassett, we say that such a fourfold is special if it contains a surface whose cohomology class does not come from the Grassmannian G(2,5). Special fourfolds correspond to a countable union of hypersurfaces in the period domain, labelled by a positive integer d, the discriminant. We describe special fourfolds for some low values of d. We also characterize those integers d for which special fourfolds do exist.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/11c29894e26a965aa70fefd71b8355485ed01ce8
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In Geometry and Topology
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In Mathematical Physics
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- O. Debarre
- K. Hori
- Alexander Perry
- Emanuele Macrì
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- I. Smith
- David Tong
Citations in the corpus
- Gushel–Mukai varieties: Linear spaces and periods (2016, methodology): “ A(X)) holds for any smooth GM fourfold or sixfold with smooth Ye A(X). This implies Theorem 5.1 in full generality. We end this section with some consequences of (28) based on results from [DK1] and [DIM]. Remark 5.28 (Period partners). In [DK1, Section 3.6], we said that smooth GM varieties of the”