Birational isomorphisms of four-dimensional quintics (Q1088740)

The author generalizes a theorem of \textit{V. A. Iskovskih} and \textit{Yu. I. Manin} [Math. USSR, Sb. 15(1971), 141-165 (1972); translation from Mat. Sb., Nov. Ser. 86(128), 140-166 (1971; Zbl 0222.14009)] by proving that any birational isomorphism between smooth hypersurfaces of degree 5 in \(P^ 5\) (over an algebraically closed field of characteristic zero) is a biregular (and even projective) isomorphism. It follows in particular the non-rationality of the smooth quintics in \(P^ 5\). - The proof goes along the lines of that of Iskovskih-Manin and uses resolution of singularities.