Normal Bundles of Lines on Hypersurfaces

Abstract

If X is a smooth hypersurface in complex projective space, the Fano variety of lines on X is stratified by the splitting type of the normal bundle of the line. We show that for general hypersurfaces, these strata have the expected dimension and, in this case, compute the class of the closure of the strata in the Chow ring of the Grassmannian of lines in projective space. For certain splitting types, we also provide upper bounds on the dimension of the strata that hold for all smooth X.