Varieties with small dual varieties. II
type: Item
instance of: scholarly article
title: Varieties with small dual varieties. II
zbMATH Open document ID: 0603.14026
DOI: 10.1215/S0012-7094-85-05247-0
author: Lawrence Ein
published in: Duke Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: 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).
reviewed by: F. L. Zak
Mathematics Subject Classification ID: 14J40
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 14M07
zbMATH DE Number: 3973046
zbMATH Keywords: dual variety
zbMATH Keywords: deformations of generic tangent hyperplane
zbMATH Keywords: positive defect
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3973046