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 global sections. We prove that D is 2-connected apart from very few cases described explicitly. We also provide a corresponding result for the 3-connectedness when D^2 \geq 10 and for the 4-connectedness when D^2 \geq 17 and D is very ample.
On the 2 and the 3-connectedness of ample divisors on a surface / M. Beltrametti, A. Lanteri. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 58:1-2(1987), pp. 109-128.
Titolo: | On the 2 and the 3-connectedness of ample divisors on a surface |
Autori: | LANTERI, ANTONIO (Ultimo) |
Parole Chiave: | projective algebraic surface; ample divisor; n-connected divisor |
Settore Scientifico Disciplinare: | Settore MAT/03 - Geometria |
Data di pubblicazione: | 1987 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/BF01169086 |
Appare nelle tipologie: | 01 - Articolo su periodico |
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