Triple-Point Defective Surfaces

Details Triple-Point Defective Surfaces Triple-Point Defective Surfaces

2009-11-06

arxiv.org/abs/0911.1222v1

Mathematics

Algebraic Geometry

The paper generalises the results in arXiv:0705.3912 using the same techniques. The assumptions both on the linear system and

Scientific paper

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.

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