On varieties as hyperplane sections

Abstract

Here we extend to the the singular (but locally complete intersection) case a theorem of L’vovsky giving a condition (" h 0 ( N X ( − 1 ) ) ⩽ n + 1 {h^0}({N_X}( - 1)) \leqslant n + 1 ") forcing a variety X ⊂ P n X \subset {{\mathbf {P}}^n} not to be a hyperplane section (except of cones). Then we give a partial extension of this criterion to the case of subvarieties of a Grassmannian.