On some invariants of cubic fourfolds.

Abstract

For a general cubic fourfold $X\subset P^5$ with Fano variety F, we compute the Hodge numbers of the locus $S\subset F$ of lines of second type and the class of the locus $V\subset F$ of triple lines, using the description of the latter in terms of flag varieties. We also give an upper bound of 6 for the degree of irrationality of the Fano scheme of lines of any smooth cubic hypersurface.