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On a theorem of Morin on the unirationality of the quartic fivefold. (English) Zbl 1041.14505

Summary: Following his original idea we give a new and simpler proof of the theorem of U. Morin [see Atti 2. Congr. Un. Mat. Ital., Bologna 1940, 298–302 (1942; Zbl 0026.42401) and Rend. Sem. Mat. Univ. Padova 21, 406–409 (1952; Zbl 0048.14401)] stating that the general quartic hypersurface \(V_m(4)\subset \mathbb{P}^{m+1}\) is unirational for \(m\geq 5\).

MSC:

14M20 Rational and unirational varieties
14J70 Hypersurfaces and algebraic geometry
14J40 \(n\)-folds (\(n>4\))
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