On 2-spannedness for the adjunction mapping |
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Authors: | E. Ballico M. Beltrametti |
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Affiliation: | (1) Dipartimento di Matematica, Università di Trento, 38050 Povo (Tn), Italy;(2) Dipartimento di Matematica, Università di Genova, Via L.B. Alberti 4, 16132 Genova, Italy |
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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. |
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