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Singular curves on a K3 surface and linear series on their normalizations
Flaminio Flamini, Andreas Leopold Knutsen, Gianluca Pacienza
In this paper, we study the Brill-Noether theory of the normalizations of singular, irreducible curves on a surface. We introduce a {\em singular} Brill-Noether number $ρ_{sin…
On varieties which are uniruled by lines
A. L. Knutsen, C. Novelli, A. Sarti
Using the -minimal model program of uniruled varieties we show that for any pair consisting of a reduced and irreducible variety of dimension and a…
Rational Curves in Calabi-Yau Threefolds
Trygve Johnsen, Andreas Leopold Knutsen
We study the set of rational curves of a certain topological type in general members of certain families of Calabi-Yau threefolds. For some families we investigate to what extent i…
Gonality and Clifford Index of curves on Surfaces
Andreas Leopold Knutsen
We show that every possible value for the Clifford index and gonality of a curve of a given genus on a surface occurs.
K3 projective models in scrolls
Trygve Johnsen, Andreas Leopold Knutsen
We study the projective models of complex K3 surfaces polarized by a line bundle L such that all smooth curves in |L| have non-general Clifford index. Such models are in a natural…
On kth-order embeddings of K3 surfaces and Enriques surfaces
Andreas Leopold Knutsen
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…