Geodesic
Generic space curves, geometry and numerology
Journal of Singularities, Tome 2 (2010), pp. 191-209

Voir la notice de l'article provenant de la source Journal of Singularities website

A projective curve Γ in P3(C) defines a stratification of P3 according to the types of the singularities of the projection of Γ from the variable point. In this paper we calculate the degrees of these strata, assuming that Γ is projection-generic in a particular sense. We use geometrical properties of the stratifications of P3 and of the blow-up BΓ of P3 along Γ (with exceptional set denoted EΓ) to introduce several auxiliary curves: more precisely, there are three 2-dimensional strata: the surface of tangents to Γ, the surface of T-secants (i.e. lines joining two points with coplanar tangents), and the surface of 3-secants. We obtain three plane curves by intersecting these with a generic plane. Three curves in EΓ were introduced in some of our earlier work. We also have three curves in ΓxΓ closely related to them. Our numerical results are obtained by applying the genus and related formulae to these curves.
DOI : 10.5427/jsing.2010.2l
Classification : 14H50, 14N10 
@article{10_5427_jsing_2010_2l,
     author = {C. T. C. Wall},
     title = {Generic space curves, geometry and numerology},
     journal = {Journal of Singularities},
     pages = {191--209},
     publisher = {mathdoc},
     volume = {2},
     year = {2010},
     doi = {10.5427/jsing.2010.2l},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2010.2l/}
}
TY  - JOUR
AU  - C. T. C. Wall
TI  - Generic space curves, geometry and numerology
JO  - Journal of Singularities
PY  - 2010
SP  - 191
EP  - 209
VL  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2010.2l/
DO  - 10.5427/jsing.2010.2l
ID  - 10_5427_jsing_2010_2l
ER  - 
%0 Journal Article
%A C. T. C. Wall
%T Generic space curves, geometry and numerology
%J Journal of Singularities
%D 2010
%P 191-209
%V 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2010.2l/
%R 10.5427/jsing.2010.2l
%F 10_5427_jsing_2010_2l
C. T. C. Wall. Generic space curves, geometry and numerology. Journal of Singularities, Tome 2 (2010), pp. 191-209. doi: 10.5427/jsing.2010.2l

Cité par Sources :