Ambrogio, Elisabetta; Romagnoli, Daniela On the non-rationality of the Fano variety of \({\mathbb{P}}^ 5\), which contains three planes two by two meeting in one point. (English) Zbl 0699.14066 Indag. Math. 51, No. 1, 15-19 (1989). We study the Fano variety W of degree \( 6\) in \({\mathbb{P}}^ 5\), complete intersection of a smooth quadric hypersurface with a smooth cubic hypersurface of \({\mathbb{P}}^ 5\), containing \(3\quad planes\) two by two meeting at least in one point. We prove that W is birationally equivalent to a smooth cubic hypersurface of \({\mathbb{P}}^ 4\), hence W is not rational. Reviewer: E.Ambrogio MSC: 14M20 Rational and unirational varieties 14N05 Projective techniques in algebraic geometry 14J30 \(3\)-folds Keywords:non-rationality; Fano variety PDFBibTeX XMLCite \textit{E. Ambrogio} and \textit{D. Romagnoli}, Indag. Math. 51, No. 1, 15--19 (1989; Zbl 0699.14066)