On kth-order embeddings of K3 surfaces and Enriques surfaces

2000/08/22 by Andreas Leopold Knutsen, Knutsen, Andreas Leopold · 1 citation
Arts and Humanities · Mathematics · #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #North African History and Literature #math.AG #msc:14J28

paper · pdf · doi:10.48550/arxiv.math/0008169

23 pages, 0 figures, slightly improved version (Section 4), added references, to appear in Manuscr. Math

openalex publication_date 2000/08/22 · arxiv created 2000/12/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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|.

Cited by

• Nef cones of Hilbert schemes of points on some K3 surfaces

Related

• Curves and line bundles on Del Pezzo surfaces
• k-very ample line bundles on Del Pezzo Surfaces
• K3 double structures on Enriques surfaces and their smoothings
• Gonality and Clifford Index of curves on K3 Surfaces
• Exceptional linear systems on curves on Enriques surfaces