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New rational cubic fourfolds arising from Cremona transformations
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New rational cubic fourfolds arising from Cremona transformations
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Are Fourier-Mukai equivalent cubic fourfolds birationally equivalent? We obtain an affirmative answer to this question for very general cubic fourfolds of discriminant 20, where we produce birational maps via the Cremona transformation defined by the Veronese surface. By studying how these maps act on the cubics known to be rational, we surprisingly found new rational examples.
Forward citations
Cited by 2 Pith papers
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Kuznetsov components ans transcendental motives of cubic fourfolds
For Fourier-Mukai partners X and Y among special cubic fourfolds, t(X) ≅ t(Y), with explicit descriptions in rational and conjecturally irrational cases plus an equivariant construction for order-3 automorphisms.
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Kuznetsov components and transcendental motives of cubic fourfolds
For special cubic fourfolds that are Fourier-Mukai partners, transcendental motives are isomorphic, with explicit descriptions in Hassett divisor families and for those with order-3 automorphisms.
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