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. [10.1007/BF01169086]
On the 2 and the 3-connectedness of ample divisors on a surface
A. LanteriUltimo
1987
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 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.
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