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Osculatory behavior and second dual varieties of Del Pezzo surfaces

Osculatory behavior and second dual varieties of Del Pezzo surfaces Let S be a smooth surface embedded in a projective space, whose general osculating space has the expected dimension. Inside the dual variety of S one can consider the second discriminant locus, which parametrizes the hyperplane sections of S having some singular point of multiplicity ≥3 . In this paper the various components of the second discriminant loci of Del Pezzo surfaces are investigated from a unifying point of view. This allows us to describe the second dual varieties of such surfaces and to understand their singular loci. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Geometry de Gruyter

Osculatory behavior and second dual varieties of Del Pezzo surfaces

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Publisher
de Gruyter
Copyright
Copyright © 2001 by the
ISSN
1615-715X
DOI
10.1515/advg.2001.021
Publisher site
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Abstract

Let S be a smooth surface embedded in a projective space, whose general osculating space has the expected dimension. Inside the dual variety of S one can consider the second discriminant locus, which parametrizes the hyperplane sections of S having some singular point of multiplicity ≥3 . In this paper the various components of the second discriminant loci of Del Pezzo surfaces are investigated from a unifying point of view. This allows us to describe the second dual varieties of such surfaces and to understand their singular loci.

Journal

Advances in Geometry – de Gruyter

Published: Nov 9, 2001

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