Non-rationality of the 4-dimensional smooth complete intersection of a quadric and a quartic not containing planes

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.