Frobenius splitting for some abelian fiber spaces
type: Item
instance of: scholarly article
title: Frobenius splitting for some abelian fiber spaces
zbMATH Open document ID: 1355.14027
author: Tomoaki Shirato
published in: Journal of Pure and Applied Algebra
publication date: 2017-01-23T00:00:00Z
review text: Let \(X\) be a smooth projective variety of characteristic \(p>0\). \(X\) is called Frobenius split if the map \(O_X\to F_*O_X\) splits as \(O_X\)-module, where \(F\) denotes the absolute Frobenius map. In this paper, the author study Frobenius split property of fibrations over curves. The main result, Theorem 1.3, is a classification of Frobenius split abelian fiber spaces over curves which has no wild fibers in terms of the degree of the top higher direct image \(R^{n-1}\pi_*O_X\), the multiplicities of multiple fibers, non-ordinary points, and the characteristic of the base field. The idea of the proof is a characterization of Frobenius split property of \(X\to C\) via the relative Frobenius morphism \(F_{X/C}\) (Proposition 1.5).
reviewed by: Linquan Ma
Mathematics Subject Classification ID: 14J27
Mathematics Subject Classification ID: 13A35
zbMATH DE Number: 6676882
zbMATH Keywords: Frobenius split variety
zbMATH Keywords: fibrations over curves
MaRDI profile type: Publication
full work available at URL: j.jpaa.2016.09.018
OpenAlex ID: W2529280412
cites work: Algebraic surfaces. Transl. from the Romanian by V. Maşek
cites work: Frobenius splitting methods in geometry and representation theory
cites work: Q4117948
cites work: On automorphisms of nodal Enriques surfaces
cites work: Surfaces of globally \(F\)-regular and \(F\)-split type
cites work: On rational connectedness of globally \(F\)-regular threefolds
cites work: Classification of two-dimensional F-regular and F-pure singularities
cites work: Q4143433
cites work: Frobenius splitting of Hilbert schemes of points on surfaces
cites work: On elliptic surfaces in characteristic p
cites work: Frobenius splitting and cohomology vanishing for Schubert varieties
cites work: Q3781217
cites work: Normal F-pure surface singularities
cites work: Ordinary varieties and the comparison between multiplier ideals and test ideals
cites work: Kummer surfaces in characteristic $2$
cites work: On the canonical bundle formula for abelian fiber spaces in positive characteristic
cites work: \(F\)-regular and \(F\)-pure normal graded rings
DOI: 10.1016/J.JPAA.2016.09.018
description: scientific article; zbMATH DE number 6676882