Polarized Pushouts for Finite Fields

Details Polarized Pushouts for Finite Fields Polarized Pushouts for Finite Fields

2002-04-19

arxiv.org/abs/math/0204243v2

Mathematics

Algebraic Geometry

Final Version. To appear in K60 volume of Communications in Algebra

Scientific paper

Let p: Y--> X be a surjection between schemes projective over the algebraic closure of a finite field. Let L be a line bundle on X such that p^*(L) is globally generated. I give a natural necessary and sufficient condition under which some positive tensor power of L is globally generated. I apply this to give a sufficient condition for semi-ampleness of nef line bundles on the moduli space of stable pointed curves, in positive characteristic.

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