Unirationality of certain complete intersections in positive characteristics
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 \(n\geq r^ 2+2r\).
scientific article; zbMATH DE number 146180