Unirationality of certain complete intersections in positive characteristics
type: Item
instance of: scholarly article
title: Unirationality of certain complete intersections in positive characteristics
zbMATH Open document ID: 0788.14043
author: Ichiro Shimada
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1993-04-01T00:00:00Z
review text: It is known that the Fermat hypersurface of degree \(q+1\) over a field of characteristic \(p\) (where \(q\) is a power of \(p)\) is unirational [cf. \textit{T. Shioda}, Math. Ann. 211, 233-236 (1974; Zbl 0276.14018) and \textit{T. Katsura}, Tôhoku Math. J., II. Ser. 31, 97-115 (1979; Zbl 0415.14022)]. In this paper a generalisation of this result is proved, to the effect that the generic complete intersection of \(r\) members of the linear system spanned by \(X_ iX_ j^ q\) \((1\leq i,j\leq n)\) is unirational, provided \(n\geq r^ 2+2r\).
reviewed by: Alexandru Buium
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 14M20
Mathematics Subject Classification ID: 14J70
Mathematics Subject Classification ID: 14G15
zbMATH DE Number: 146180
zbMATH Keywords: unirationality
zbMATH Keywords: characteristic \(p\)
zbMATH Keywords: Fermat hypersurface
zbMATH Keywords: complete intersection
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227304
OpenAlex ID: W2019951835
cites work: Q3211457
cites work: Factor Representations and Factor States on a C*-Algebra
cites work: An example of unirational surfaces in characteristic \(p\)
cites work: On Fermat varieties
cites work: Q5615218
DOI: 10.2748/TMJ/1178227304
description: scientific article; zbMATH DE number 146180