Rationality of the field of invariants of a faithful four-dimensional representation of the icosahedral group (Q1110608)

The group \(G=SL_ 2(F_ 5)\) has two complex 4-dimensional and irreducible representations and one of them (call it \(\phi)\) is exact. Using \(\phi\) we get an action of G on \({\mathbb{C}}P^ 3\). The authors prove that the factor-variety \({\mathbb{C}}P^ 3/G\) is rational. The proof uses elements of the theory of threefolds.