Eckardt loci on hypersurfaces

2015-04-17T08:20:35Z (GMT) by Izzet Coskun Artie Prendergast
We compute the dimensions and cohomology classes of the loci on a general hypersurface where the second fundamental form has rank at most r. We also determine the number of hypersurfaces in a general pencil in P n, with n = `q+1 2 ´ , that contain a point where the second fundamental form has rank n − 1 − q. These results generalize many classical formulae.