Triple-Point Defective Regular Surfaces

Details Triple-Point Defective Regular Surfaces Triple-Point Defective Regular Surfaces

2007-05-26

arxiv.org/abs/0705.3912v2

Mathematics

Algebraic Geometry

The results of this paper have been generalised in the paper Triple point defective surfaces (arXiv:0911.1222) by the same aut

Scientific paper

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.

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