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 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 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.
Chiantini, L., Markwig, T. (2010). Triple-point defective surfaces. ADVANCES IN GEOMETRY, 10, 527-547 [10.1515/ADVGEOM.2010.030].
Triple-point defective surfaces
CHIANTINI, LUCA;
2010-01-01
Abstract
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 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 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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https://hdl.handle.net/11365/17868
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