Abstract
Let S be a smooth projective surface over C polarized by a 2-very ample line bundle L=O S(L), i.e. for any 0-dimensional subscheme (Z,O Z ) of length 3 the restriction map Γ(L)→Γ(L⊗O Z) is a surjection. This generalization of very ampleness was recently introduced by M. Beltrametti and A.J. Sommese.
The authors prove that, if L·L≥13, the adjoint line bundleK S⊗L is 2-very ample apart from a list of well understood exceptions and up to contracting down the smooth rational curves E such that E·E=−1, L·E=2.
The appendix contains an inductive argument in order to extend the result in higher dimension.
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