, Volume 61, Issue 4, pp 447-458

On 2-spannedness for the adjunction mapping

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Abstract

LetL be a line bundle on a smooth connected projective manifold X of dimension n. We extend to any dimension the definition of k-spannedness forL; this is a notion of “k-th order embedding” which was recently given in the case of curves and surfaces. Then, by a reduction to the surfaces case, we prove that the adjoint bundle Kx+(n−1)L is 2-spanned ifL is (at least) 3-spanned.