Base locus of linear systems on the blowing-up of ℙ³ along at most 8 general points

Cindy De Volder and Antonio Laface

Vol. 223 (2006), No. 1, 17–34

DOI: 10.2140/pjm.2006.223.17

Abstract

Consider a (nonempty) linear system of surfaces of degree d in ℙ³ through at most 8 multiple points in general position and let ℒ denote the corresponding complete linear system on the blowing-up X of ℙ³ along those general points. Then we determine the base locus of such linear systems ℒ on X.

Keywords

base locus, linear systems, fat points, projective space

Mathematical Subject Classification 2000

Primary: 14C20

Milestones

Received: 6 April 2004

Revised: 28 July 2004

Accepted: 10 January 2005

Published: 1 January 2006