On the normal class of curves and surfaces (original) (raw)

Pré-Publication, Document De Travail Année : 2014

Résumé

We are interested in the normal class of an algebraic surface S of the complex projective space P^3, that is the number of normal lines to S passing through a generic point of P^3. Thanks to the notion of normal polar, we state a formula for the normal class valid for a general surface S. We give a generic result and we illustrate our formula with examples. 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. This last formula gives directly the normal class of any cylinder and of any surface of revolution of P^3.

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https://hal.science/hal-00953669

Soumis le : mercredi 21 mai 2014-17:48:39

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

Archivage à long terme le : jeudi 21 août 2014-12:25:23

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)

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Identifiants

HAL Id : hal-00953669 , version 2
ARXIV : 1402.7266

Citer

Alfrederic Josse, Françoise Pene. On the normal class of curves and surfaces. 2014. ⟨hal-00953669v2⟩

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