Let S be a complex projective surface endowed with an ample and spanned line bundle L. Assume that (S,L) does not belong to some special classes and that cl(L)2≥10. We prove that(KS⊗L)·KS≤-3 and |L| contains a trigonal curve (of genus≥4) iff either (S,L) is a rational surface ruled by cubics, or the g13 of C is cut out by |KS⊗-1|. This result applies to surface having a hyperplane section which is a trigonal curve. © 1989 Springer-Verlag.
Brivio, S., Lanteri, A. (1989). On complex projective surfaces with trigonal hyperplane sections. MANUSCRIPTA MATHEMATICA, 65(1), 83-92 [10.1007/BF01168368].
On complex projective surfaces with trigonal hyperplane sections
Brivio S.
;
1989
Abstract
Let S be a complex projective surface endowed with an ample and spanned line bundle L. Assume that (S,L) does not belong to some special classes and that cl(L)2≥10. We prove that(KS⊗L)·KS≤-3 and |L| contains a trigonal curve (of genus≥4) iff either (S,L) is a rational surface ruled by cubics, or the g13 of C is cut out by |KS⊗-1|. This result applies to surface having a hyperplane section which is a trigonal curve. © 1989 Springer-Verlag.
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