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Linear systems with removable base loci

In this paper, we will give a simple proof of a famous result of Zariski and Fujita on linear systems with removable base loci. The novelty of our proof is that it is based on studying the canonical nonexact Koszul complex associated with the linear system. We believe that these methods will also be useful in studying other problems on linear systems. We should point out that Gruson, Lazarsfeld and Peskine ([3]) had used nonexact complexes to study the syzygies of space curves. Also the author and Lazarsfeld ([I]) had also used nonexact complexes to study syzygies of higher dimensional varieties. We would like to thank R. Lazarsfeld for many helpful discussions.