Cubic fourfolds with an involution

There are three types of involutions on a cubic fourfold; two anti-symplectic type, and one symplectic. Here we show that cubics with exhibit the full range behaviour in relation to rationality conjectures. Namely, general fourfold symplectic involution has no associatedK3K3surface is conjecturely irrational. In contrast, particular an encoding="application/x-tex">K3, fact rational. We such contained intersection all non-empty Hassett divisors; call maximal. study algebraic transcendental lattices for both lattice theoretically geometrically.