ar X iv : 0 70 5 . 39 12 v 1 [ m at h . A G ] 2 6 M ay 2 00 7 TRIPLE - POINT DEFECTIVE REGULAR SURFACES
نویسنده
چکیده
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) triplepoint 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.
منابع مشابه
ar X iv : 0 70 5 . 39 13 v 1 [ m at h . A G ] 2 6 M ay 2 00 7 TRIPLE - POINT DEFECTIVE RULED SURFACES
In [ChM07] we studied triple-point defective very ample linear systems on regular surfaces, and we showed that they can only exist if the surface is ruled. In the present paper we show that we can drop the regularity assumption, and we classify the triplepoint defective very ample linear systems on ruled surfaces. Let S be a smooth projective surface, K = KS the canonical class and L a divisor ...
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