Analysis, Geometry, and Dynamical Systems Seminar   RSS

12/07/2017, 15:00 — 16:00 — Room P3.31, Mathematics Building
Francesco Russo, University of Catania

Some loci of rational cubic fourfolds

We shall report on joint work with Michele Bolognesi and Giovanni Staglianò on the irreducible divisor $\mathcal C_{14}$ inside the moduli space of smooth cubic hypersurfaces in $\mathbb P^5$. A general point of $\mathcal C_{14}$ is, by definition, a smooth cubic fourfold containing a smooth quartic rational normal scroll (or, equivalently, a smooth quintic del Pezzo surfaces) so that it is rational. We shall prove that every cubic fourfold contained in $\mathcal C_{14}$ is rational.

In passing we shall review and put in modern terms some ideas of Fano, yielding a geometric insight to some known results on cubic fourfolds, e.g. the Beauville-Donagi isomorphism, and discuss also the connections of our results with the recent examples about the bad behavior of rationality in smooth families of fourfolds.