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On the polar varieties of ruled hypersurfaces
Published online by Cambridge University Press: 09 November 2016
Abstract
The aim of this work is to characterise the k-polar variety Pk(X) of an (n − 1)-ruled hypersurface X ⊂ ℂn+1. More precisely, we prove that Pk(X) is empty for all k >1 and the first polar variety is empty or it is an (n − 2)-ruled variety in ℂn+1, whose multiplicity is obtained by the multiplicity of the base curve and the multiplicity of one directrix of X. As a consequence we obtain the Euler obstruction Eu0(X) of X and, in addition, we exhibit (n − 1)-ruled hypersurfaces such that Eu0(X) = m, for any prescribed positive integer m.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 164 , Issue 2 , March 2018 , pp. 193 - 204
- Copyright
- Copyright © Cambridge Philosophical Society 2016
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