COSKUN, I. and PRENDERGAST-SMITH, A., 2015. Eckardt loci on hypersurfaces. Communications in Algebra, 43(8), pp. 3083-3101.
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 =
that contain a point where the second fundamental form has rank n − 1 − q. These results generalize many classical formulae.
This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 4th Jun 2015, available online: http://dx.doi.org/10.1080/00927872.2014.910798
During the preparation of this article the first author was partially supported by the NSF CAREER grant DMS-0950951535, and an Alfred P.
Sloan Foundation Fellowship.