Paranjape, Kapil H.; Srinivas, V. Unirationality of the general complete intersection of small multidegree. (English) Zbl 0807.14039 Kollár, János (ed.), Flips and abundance for algebraic threefolds. A summer seminar at the University of Utah, Salt Lake City, 1991. Paris: Société Mathématique de France, Astérisque. 211, 241-254 (1992). [This is chapter 23 of the Summer Seminar at Utah Univ. (loc. cit.).]It was shown by U. Morin [Atti II. Congr. Un. Mat. Ital., Bologna 1940, 298-302 (1942; Zbl 0026.42401)] that the general hypersurface of degree \(d\) and dimension sufficiently large is unirational once it contains a linear space of sufficiently large dimension defined over the given field, this latter condition being always true over an algebraically closed field. This was further generalized by A. Predonzan [Rend. Sem. Mat. Univ. Padova 18, 163-176 (1949; Zbl 0033.016)] to include the case of complete intersections. In the present paper the authors present a proof of these results and some related results.For the entire collection see [Zbl 0782.00075]. Reviewer: V.L.Popov (Ann Arbor) Cited in 1 ReviewCited in 3 Documents MSC: 14M10 Complete intersections 14J70 Hypersurfaces and algebraic geometry 14M20 Rational and unirational varieties Keywords:hypersurface; complete intersections Citations:Zbl 0026.42401; Zbl 0033.016 PDFBibTeX XMLCite \textit{K. H. Paranjape} and \textit{V. Srinivas}, in: Flips and abundance for algebraic threefolds. A summer seminar at the University of Utah, Salt Lake City, 1991. Paris: Société Mathématique de France. 241--254 (1992; Zbl 0807.14039)