Rational cubic fourfolds with associated singular K3 surfaces

Abstract

Generalizing a recent construction of Yang and Yu, we study to what extent one can intersect Hassett's Noether-Lefschetz divisors ${\mathcal{C}}_d$ in the moduli space of cubic fourfolds $\mathcal{C}$. In particular, we exhibit arithmetic conditions on 20 indexes $d_1,\dots ,d_{20}$ that assure that the divisors ${\mathcal{C}}_{d_1},\dots ,{\mathcal{C}}_{d_{20}}$ all intersect one another. This allows us to produce examples of rational cubic fourfolds with an associated K3 surface with rank 20 Néron-Severi group, i.e. a singular K3 surface.

arXiv comment14 pages

References in corpus (5)

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

Cited by in corpus (2)

• A family of special cubic fourfolds with motive of abelian type
• On lattice polarizable cubic fourfolds