Varieties with small dual varieties. II (Q1082394)

In the notations of part I of this paper [see the preceding review], suppose that def X\(>0\) and let H be a generic tangent hyperplane. Then H is tangent to X along a def X-dimensional linear subspace \(L\subset X\). The author studies deformations of L in X. In particular, it is shown that \(def X=\dim X-2\Rightarrow X\quad is\quad a\quad scroll\) and \(def X=k\geq \dim X\Rightarrow X\quad is\quad a\quad {\mathbb{P}}^{(\dim X+k)}- bundle.\) The author also classifies all varieties with positive defect whose dimension does not exceed 6 (besides projective bundles, the only examples are the Grassmann variety \(G(4,1)^ 6\subset {\mathbb{P}}^ 9\) and its hyperplane section).