Degeneration of linear systems through fat points on K3 surfaces

Details Degeneration of linear systems through fat points on K3 surfaces Degeneration of linear systems through fat points on K3 surfaces

2003-10-15

arxiv.org/abs/math/0310219v1

Mathematics

Algebraic Geometry

12 pages, LaTeX

Scientific paper

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 P^3.

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