Non-rationality of the  4-dimensional smooth complete intersection of

I. A. Cheltsov

Sbornik. Mathematics, Tome 194 (2003) no. 11, pp. 1679-1699

Résumé

The non-rationality and the birational superrigidity is proved for the 4-dimensional smooth complete intersection of a quadric and a quartic in ${\mathbb P}^6$ that contains no 2-dimensional linear subspace of ${\mathbb P}^6$. It is also proved that such an intersection is not birationally isomorphic to an elliptic fibration.

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