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Varieties with small dual varieties. II. (English) Zbl 0603.14026
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).
Reviewer: F.L.Zak

MSC:
14J40 \(n\)-folds (\(n>4\))
14N05 Projective techniques in algebraic geometry
14J10 Families, moduli, classification: algebraic theory
14M07 Low codimension problems in algebraic geometry
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