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

1993/11/30 by Takao Fujita, Fujita, Takao
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9311013

23 pages, amstex

arxiv created 1993/11/30 · arxiv updated 2009/11/30

Abstract

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≥3 for any curve C passing x, B²S≥7 for any surface S containing x, and B³≥51. Then K+B is spanned at x. (Ein-Lazarsfeld proved the assertion assuming B³≥92.) Corollary: K+3L is spanned if L is an ample line bundle with L³>1.

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