On kth-order embeddings of K3 surfaces and Enriques surfaces
Abstract
Description
We give necessary and sufficient conditions for a big and nef line bundle L of any degree on a K3 surface or Enriques surface to be k-very ample and k-spanned. Furthermore, we give necessary and sufficient conditions for a spanned and big line bundle on a K3 surface to be birationally k-very ample and birationally k-spanned, and relate these concepts to the Clifford index and gonality of smooth curves in |L|.
23 pages, 0 figures, slightly improved version (Section 4), added references, to appear in Manuscr. Math
23 pages, 0 figures, slightly improved version (Section 4), added references, to appear in Manuscr. Math