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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

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
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