2021/03/16 by Song Yang, Xun Yu, Yang, Song +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2103.09132
openalex publication_date 2021/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend non-emtpyness and irreducibility of Hassett divisors to the moduli spaces of M-polarizable cubic fourfolds for higher rank lattices M, which in turn provides a systematic approach for describing the irreducible components of intersection of Hassett divisors. We show that Fermat cubic fourfold is contained in every Hassett divisor, which yields a new proof of Hassett's existence theorem of special cubic fourfolds. We obtain an algorithm to determine the irreducible components of the intersection of any two Hassett divisors and we give new examples of rational cubic fourfolds. Moreover, we derive a numerical criterion for the algebraic cohomology of a cubic fourfold having an associated K3 surface and answer a question of Laza by realizing infinitely many rank 11 lattices as the algebraic cohomologies of cubic fourfolds having no associated K3 surfaces.