On triple curves through a rational triple point of a surface

M. R. Gonzalez-Dorrego¹

¹Departamento de Matemáticas Universidad Autónoma de Madrid 28049 Madrid, Spain

Annales Polonici Mathematici, Tome 88 (2006) no. 1, pp. 1-17

Résumé

Let $k$ be an algebraically closed field of characteristic $0$. Let $C$ be an irreducible nonsingular curve in ${{\mathbb P}}^n$ such that $3C=S\cap F$, where $S$ is a hypersurface and $F$ is a surface in ${{\mathbb P}}^n$ and $F$ has rational triple points. We classify the rational triple points through which such a curve $C$ can pass (Theorem 1.8), and give an example (1.12). We only consider reduced and irreducible surfaces.

Détail

DOI : 10.4064/ap88-1-1

Keywords: algebraically closed field characteristic irreducible nonsingular curve mathbb cap where hypersurface surface mathbb has rational triple points classify rational triple points through which curve pass theorem example only consider reduced irreducible surfaces