Linear systems on generic K3 surfaces

2003/09/04 by Cindy De Volder, De Volder, Cindy, Antonio Laface +1
Mathematics · #14C20 #14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C20 #msc:14J28

paper · pdf · doi:10.48550/arxiv.math/0309073

8 pages, LaTeX

arxiv created 2003/09/04 · arxiv updated 2009/12/01

Abstract

In this paper we prove the equivalence of two conjectures on linear systems through fat points on a generic K3 surface. The first conjecture is exactly as Segre conjecture on the projective plane. Whereas the second characterizes such linear system and can be compared to the Gimigliano-Harbourne-Hirschowitz conjecture.

Related

• Recent results on linear systems on generic K3 surfaces
• Special homogeneous linear systems on Hirzebruch surfaces
• Degeneration of linear systems through fat points on K3 surfaces
• Interpolation of fat points on K3 and abelian surfaces
• Reduction method for linear systems of plane curves with base fat points