On the 2 very ampleness of the adjoint bundle (original) (raw)

With an Appendix by E. Ballico Let S be a smooth projective surface over C polarized by a 2-very ample line bundle L=Os(L), i.e. for any 0-dimensional subscheme (Z,Oz) of length 3 the restriction map F(L)--->F(L| 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 bundle Ks| 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.