Normal class and normal lines of algebraic surfaces

Alfrederic Josse (1) , Françoise Pene (1)

1 LM - Laboratoire de mathématiques de Brest

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 define the orthogonal indidence variety and compute the Schubert class of the variety of projective normal lines 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.

Mots clés: projective normal; class; Plücker; Grassmannian; Puiseux

Domaines: Géométrie algébrique [math.AG]

Alfrederic Josse, Françoise Pene. Normal class and normal lines of algebraic surfaces. 2014. ⟨hal-00953669v3⟩