A Remark on Classical Pluecker’s formulae
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 5, pp. 959-967.

Pour toute courbe réduite C2, on introduit la notion de nombre des points de rebroussement (cusps) virtuels cv et celle de nombre des points doubles ordinaires (nodes) virtuels nv. Ces deux nombres sont positifs ou nuls et ils coïncident avec le nombre des points singuliers du type respectif lorsque ce sont les seules singularités de la courbe. De plus, si C^ est la courbe duale d’une courbe irréducible C, et si n^v et c^v designent le nombre de singularités virtuelles de C^ du type respectif, alors les nombres entiers cv, nv, c^v, n^v vérifient les formules de Plücker classiques.

For any reduced curve C2, we introduce the notions of the number of its virtual cusps cv and the number of its virtual nodes nv. We prove that the numbers cv and nv are non-negative and if C is a curve with only ordinary cusps and nodes as its singular points, then cv is the number of its ordinary cusps and nv is the number of its ordinary nodes. In addition, if C^ is the dual curve of an irreducible curve C and n^v and c^v are the numbers of its virtual nodes and virtual cusps, then the integers cv, nv, c^v, n^v satisfy classical Plücker’s formulae.

Publié le :
DOI : 10.5802/afst.1517

Vik.S. Kulikov 1

1 Steklov Mathematical Institute
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Vik.S. Kulikov. A Remark on Classical Pluecker’s formulae. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 5, pp. 959-967. doi : 10.5802/afst.1517. https://afst.centre-mersenne.org/articles/10.5802/afst.1517/

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