## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Linear systems on generic $K3$ surfaces

#### 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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 12, Number 4 (2005), 481-489.

Dates
First available in Project Euclid: 5 December 2005

https://projecteuclid.org/euclid.bbms/1133793336

Digital Object Identifier
doi:10.36045/bbms/1133793336

Mathematical Reviews number (MathSciNet)
MR2205992

Zentralblatt MATH identifier
1054.14011

#### Citation

De Volder, Cindy; Laface, Antonio. Linear systems on generic $K3$ surfaces. Bull. Belg. Math. Soc. Simon Stevin 12 (2005), no. 4, 481--489. doi:10.36045/bbms/1133793336. https://projecteuclid.org/euclid.bbms/1133793336