New rational cubic fourfolds arising from Cremona transformations

Abstract

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.

41 pages. Final version, accepted by Algebraic Geometry

References in corpus (3)

• Congruences of 5-secant conics and the rationality of some admissible cubic fourfolds
• Trisecant Flops, their associated K3 surfaces and the rationality of some Fano fourfolds
• Rational cubic fourfolds in Hassett divisors

Cited by in corpus (1)

• On lattice polarizable cubic fourfolds