On lattice polarizable cubic fourfolds

We extend non-emptyness and irreducibility of Hassett divisors to the moduli spaces M-polarizable cubic fourfolds for higher rank lattices M, which in turn provides a systematic approach describing irreducible components intersection divisors. show that Fermat fourfold is contained every divisor, yields new proof Hassett’s existence theorem special fourfolds. obtain an algorithm determine any two we give examples rational Moreover, derive numerical criterion algebraic cohomology having associated K3 surface answer question Laza by realizing infinitely many 11 as cohomologies no surfaces.