Remarks on Ein-Lazarsfeld criterion of spannedness of adjoint bundles of polarized threefolds

Details Remarks on Ein-Lazarsfeld criterion of spannedness of adjoint bundles of polarized threefolds Remarks on Ein-Lazarsfeld criterion of spannedness of adjoint bundles of polarized threefolds

1993-11-30

arxiv.org/abs/alg-geom/9311013v1

Mathematics

Algebraic Geometry

23 pages, amstex

Scientific paper

Let B be a nef and big line bundle on a smooth complex threefold X with
canonical bundle K. Let x be a point on X and suppose that BC\ge3 for any curve
C passing x, B^2S\ge7 for any surface S containing x, and B^3\ge51. Then K+B is
spanned at x. (Ein-Lazarsfeld proved the assertion assuming B^3\ge92.)
Corollary: K+3L is spanned if L is an ample line bundle with L^3>1.

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