Triple-Point Defective Surfaces

Abstract

In this paper we study the linear series $|L-3p|$ of hyperplane sections with a triple point $p$ on a surface $S$ embedded via a very ample line bundle $L$ for a \emph{general} point $p$. If this linear series does not have the expected dimension we call $(S,L)$ \emph{triple-point defective}. We show that on a triple-point defective 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.

The paper generalises the results in arXiv:0705.3912 using the same techniques. The assumptions both on the linear system and on the surface have been weakened. The interested reader should consult this new paper instead of the older one