On triple curves through a rational triple point of a surface
Volume 88 / 2006
Annales Polonici Mathematici 88 (2006), 1-17
MSC: 14H45, 14J17, 14J25.
DOI: 10.4064/ap88-1-1
Abstract
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.
