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Proceedings of the American Mathematical Society

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On varieties as hyperplane sections

Author: E. Ballico
Journal: Proc. Amer. Math. Soc. 120 (1994), 405-411
MSC: Primary 14N05; Secondary 14M10
MathSciNet review: 1172946
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Abstract: Here we extend to the the singular (but locally complete intersection) case a theorem of L’vovsky giving a condition ("${h^0}({N_X}( - 1)) \leqslant n + 1$") forcing a variety $X \subset {{\mathbf {P}}^n}$ 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.

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Keywords: Hyperplane section, projective variety, normal bundle, Grassmannian, deformation theory
Article copyright: © Copyright 1994 American Mathematical Society