Relative Canonical Sheaves of a Family of Curves

2002/11/18 by Jongmin Lee
Mathematics · #math.AG #msc:14D99

paper · pdf

published as Journal of Algebra, Volume 286(2005), no. 2, 341-360 · 16 pages

arxiv created 2002/11/18 · arxiv updated 2009/11/30

Abstract

In this paper we show that the relative canonical sheaf of a relatively minimal fibration of curves over a curve is semi-ample ; in fact, its m-tensored product is base point free for any m > 1. We use Koszul cohomology with it to prove that the relative canonical ring of the fibration is generated in degree up to five.

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