Effective non-vanishing for algebraic surfaces in positive characteristic
type: Item
instance of: scholarly article
title: Effective non-vanishing for algebraic surfaces in positive characteristic
zbMATH Open document ID: 1105.14054
author: Qihong Xie
published in: Journal of Algebra
publication date: 2006-12-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0509086
review text: The author proves a few non-vanishing theorems on algebraic surfaces defined over a field of positive characteristic. These are sort of the generalizations to the original conjectures of Ambro, Kawamata et al. The original non-vanishing problem in the zero characteristic case was solved by \textit{Y. Kawamata} [Asian J. Math. 4, No.~1, 173--181 (2000; Zbl 1060.14505)] provided the variety is a surface or is a minimal threefold. There is also a generalization of Kawamata's conjecture / result to the \(\mathbb Q\)-divisors on surfaces by \textit{J. A. Chen, M. Chen} and the reviewer [J. Algebra 293, 363--384 (2005; Zbl 1093.14010)]. The author also gives examples on ruled surfaces to show that Kawamata-Viehweg vanishing or Kollar vanishing may not hold when the characteristic is positive.
Mathematics Subject Classification ID: 14J26
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14F17
zbMATH DE Number: 5078323
reviewed by: De-Qi Zhang
MaRDI profile type: Publication
OpenAlex ID: W2094013427
arXiv ID: math/0509086
cites work: Ladders on Fano varieties
cites work: Algebraic surfaces. Transl. from the Romanian by V. Maşek
cites work: Enriques' classification of surfaces in char p. III
cites work: A non-vanishing theorem for \(\mathbb{Q}\)-divisors on surfaces
cites work: Q4440487
cites work: Q4143433
cites work: Q4699504
cites work: On effective non-vanishing and base-point-freeness.
cites work: Q3825176
cites work: Higher direct images of dualizing sheaves. I
cites work: Q4847164
cites work: Q4212603
cites work: Quasi-elliptic surfaces in characteristic three
cites work: Threefolds whose canonical bundles are not numerically effective
cites work: Q5582831
cites work: Duality between D(X) and with its application to picard sheaves
cites work: Q3882568
cites work: Q4135685
cites work: Geography for surfaces of general type in positive characteristic
cites work: On the Behavior of Extensions of Vector Bundles Under the Frobenius Map
cites work: On pseudo-effectivity of the second Chern classes for terminal threefolds
DOI: 10.1016/J.JALGEBRA.2006.06.008
description: scientific article