Normal class and normal lines of algebraic hypersurfaces (original) (raw)

Pré-Publication, Document De Travail Année : 2014

Résumé

We are interested in the normal class of an algebraic hypersurface Z of the complex projective space P^n, that is the number of normal lines to Z passing through a generic point of P^n. Thanks to the notion of normal polar, we state a formula for the normal class valid for a general hypersurface Z of P^n. We give a generic result and we illustrate our formula with examples in P^n. We define the orthogonal indidence variety and compute the Schubert class of the variety of projective normal lines to a surface of P^3 in the Show ring of G(1,3). We complete our work with a generalization of Salmon's formula for the normal class of a Plucker curve to any planar curve with any kind of singularity.

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https://hal.science/hal-00953669

Soumis le : samedi 2 avril 2016-15:52:31

Dernière modification le : vendredi 9 janvier 2026-11:22:07

Archivage à long terme le : dimanche 3 juillet 2016-12:12:19

Dates et versions

hal-00953669 , version 1 (28-02-2014)

hal-00953669 , version 2 (21-05-2014)

hal-00953669 , version 3 (12-10-2014)

hal-00953669 , version 4 (02-04-2016)

Licence

Identifiants

HAL Id : hal-00953669 , version 4
ARXIV : 1402.7266

Citer

Alfrederic Josse, Françoise Pene. Normal class and normal lines of algebraic hypersurfaces. 2014. ⟨hal-00953669v4⟩

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