On some invariants of cubic fourfolds

Abstract

For a general cubic fourfold Xsubset mathbb {P}^5 with Fano variety F, we compute the Hodge numbers of the locus Ssubset F of lines of second type and the class of the locus Vsubset 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.