Let k be an algebraically closed field of characteristic 0. Let C be an irreducible nonsingular curve in ℙⁿ such that 3C = S ∩ F, where S is a hypersurface and F is a surface in ℙⁿ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap88-1-1,
author = {M. R. Gonzalez-Dorrego},
title = {On triple curves through a rational triple point of a surface},
journal = {Annales Polonici Mathematici},
volume = {89},
year = {2006},
pages = {1-17},
zbl = {1095.14035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap88-1-1}
}
M. R. Gonzalez-Dorrego. On triple curves through a rational triple point of a surface. Annales Polonici Mathematici, Tome 89 (2006) pp. 1-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap88-1-1/