Degeneration of linear systems through fat points on K3 surfaces

2003/10/15 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/0310219

12 pages, LaTeX

arxiv created 2003/10/15 · arxiv updated 2009/12/01

Abstract

In this paper we introduce a technique to degenerate K3 surfaces and linear systems through fat points in general position on K3 surfaces. Using this degeneration we show that on generic K3 surfaces it is enough to prove that linear systems with one fat point are non-special in order to obtain the non-speciality of homogeneous linear systems through n = 4^u9^w fat points in general position. Moreover, we use this degeneration to obtain a result for homogeneous linear systems through n = 4^u9^w fat points in general position on a general quartic surface in P³.

Related

• Recent results on linear systems on generic K3 surfaces
• Linear systems on generic K3 surfaces
• Interpolation of fat points on K3 and abelian surfaces
• Linear systems in P³ with low degrees and low multiplicities
• On a class of special linear systems of P³