Non-rationality of the \({\mathfrak S}_6\)-symmetric quartic threefolds. (English) Zbl 1327.14220

Beauville, A.

Rend. Semin. Mat., Univ. Politec. Torino 71, No. 3-4, 385-388 (2013).

Summary: We prove that the quartic hypersurfaces defined by \(\sum x_i= t \sum x^4_i-(\sum x^2_i)^2= 0\) in \(\mathbb{P}^5\) are not rational for \(t\neq 0,2,4,6,{10\over 7}\).

MSC:

14M20	Rational and unirational varieties
14E08	Rationality questions in algebraic geometry
14K30	Picard schemes, higher Jacobians