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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].

MSC:

14M10 Complete intersections
14J70 Hypersurfaces and algebraic geometry
14M20 Rational and unirational varieties
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