On the degree of Fano schemes of linear subspaces on hypersurfaces

Abstract

Abstract. In this paper we propose and prove an explicit formula for computing the degree of Fano schemes of linear subspaces on general hypersurfaces. The method used here is based on the localization theorem and Bott's residue formula in equivariant intersection theory.

On Fano Schemes of Complete Intersections

“…1,2] says, in particular, that one can compute the degree of a zero-dimensional cycle class on a smooth projective variety X in terms of local contributions given by the fixed point loci of a torus action on X. Here we follow the treatment in [27] based on [12], [20], and [38] and adapted to our setting.…”