When is the Albanese morphism an algebraic fiber space in positive characteristic?
Algebraic Geometry
2020-07-23 v2
Abstract
In this paper, we study the Albanese morphisms in positive characteristic. We prove that the Albanese morphism of a variety with nef anti-canonical divisor is an algebraic fiber space, under the assumption that the general fiber is -pure. Furthermore, we consider a notion of -splitting for morphisms, and investigate it of the Albanese morphisms. We show that an -split variety has -split Albanese morphism, and that the -split Albanese morphism is an algebraic fiber space. As an application, we provide a new characterization of abelian varieties.
Keywords
Cite
@article{arxiv.1704.08652,
title = {When is the Albanese morphism an algebraic fiber space in positive characteristic?},
author = {Sho Ejiri},
journal= {arXiv preprint arXiv:1704.08652},
year = {2020}
}
Comments
24 pages, v2: an error in Proposition 5.11 corrected, and the proof of Lemma 4.5 corrected