On the 2 and the 3-connectedness of ample divisors on a surface |
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Authors: | Mauro Beltrametti Antonio Lanteri |
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Affiliation: | (1) Istituto Matematico-Università, Via L.B. Alberti, 4, I-16132 Genova, Italy;(2) Dipartimento di Matematica, F. Enriques-Università, Via C. Saldini, 50, I-20133 Milano, Italy |
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Abstract: | Let X be a nonsingular complex projective surface and let D be an ample divisor on X such that the associated invertible sheaf is spanned by its global sections. We prove that D is 2-connected apart from a few cases we explicitly describe. We also provide a corresponding result for the 3-connectedness when D210 and for the 4-connectedness when D217 and D is very ample. |
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