Relative Canonical Sheaves of a Family of Curves

Details Relative Canonical Sheaves of a Family of Curves Relative Canonical Sheaves of a Family of Curves

2002-11-18

arxiv.org/abs/math/0211274v1

Journal of Algebra, Volume 286(2005), no. 2, 341-360

Mathematics

Algebraic Geometry

16 pages

Scientific paper

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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