Rational cubic fourfolds with associated singular K3 surfaces

2020/04/17 by Hanine Awada, Awada, Hanine · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2004.08446

Abstract

Generalizing a recent construction of Yang and Yu, we study to what extent one can intersect Hassett's Noether-Lefschetz divisors C_d in the moduli space of cubic fourfolds C. In particular, we exhibit arithmetic conditions on 20 indexes d₁,…, d₂₀ that assure that the divisors C_d1,…,C_d₂₀ 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.

Citations

• Rational fibered cubic fourfolds

Cited by

• On lattice polarizable cubic fourfolds

Related

• Variety of power sums and divisors in the moduli space of cubic fourfolds
• Rational cubic fourfolds in Hassett divisors
• Hodge theory and derived categories of cubic fourfolds
• Moduli of Cubic fourfolds and reducible OADP surfaces
• K3 surfaces associated to a cubic fourfold