Higher dimensional polarized varieties with non-integral nefvalue.
Applications of the Ein-Lazarsfeld cirterion for spannedness of adjoint bundles.
On the preservation of k-very ampleness under adjunction.
On the adjunction theoretic classification of projective varieties.
On generation of jets for vector bundles.
We introduce and study the k-jet ampleness and the k-jet spannedness for a vector bundle, E, on a projective manifold. We obtain different characterizations of projective space in terms of such positivity properties for E. We compare the 1-jet ampleness with different notions of very ampleness in the literature.
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