Triple-Point Defective Regular Surfaces
Algebraic Geometry
2009-11-06 v2
Abstract
In this paper we study the linear series |L-3p| of hyperplane sections with a triple point p of a surface S embedded via a very ample line bundle L for a general point p. If this linear series does not have the expected dimension we call (S,L) triple-point defective. We show that on a triple-point defective regular surface through a general point every hyperplane section has either a triple component or the surface is rationally ruled and the hyperplane section contains twice a fibre of the ruling.
Cite
@article{arxiv.0705.3912,
title = {Triple-Point Defective Regular Surfaces},
author = {Luca Chiantini and Thomas Markwig},
journal= {arXiv preprint arXiv:0705.3912},
year = {2009}
}