New examples of rational Gushel-Mukai fourfolds. (English) Zbl 1450.14006
Summary: We construct new examples of rational Gushel-Mukai fourfolds, giving more evidence for the analog of the Kuznetsov Conjecture for cubic fourfolds: a Gushel-Mukai fourfold is rational if and only if it admits an associated \(K3\) surface.
MSC:
| 14F08 | Derived categories of sheaves, dg categories, and related constructions in algebraic geometry |
| 14J60 | Vector bundles on surfaces and higher-dimensional varieties, and their moduli |
| 14J35 | \(4\)-folds |
| 14J28 | \(K3\) surfaces and Enriques surfaces |
| 14M20 | Rational and unirational varieties |
Software:
Macaulay2References:
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