A characterization of secant varieties of Severi varieties among cubic hypersurfaces

Abstract

It is shown that an irreducible cubic hypersurface with nonzero Hessian and smooth singular locus is the secant variety of a Severi variety if and only if its Lie algebra of infinitesimal linear automorphisms admits a nonzero prolongation.

17 pages. We give a new proof of Theorem 2.9 bypassing the imprecisely stated Lemma 2.12 in the previous version. The validity of the results of the paper is not affected