The Nieto quintic is Janus-like (Q1807894)

The Nieto quintic \(N\) is the subvariety of \(\mathbb{P}^5\) of equations \(\sum^5_{i=0}x_i= \sum^5_{i=0} x_0\dots \widehat x_i\dots x_5=0\). In this paper the author studies a birational model \(\overline N\) of \(N\) (obtained by blowing up some singular points and blowing down some lines) and he proves that \(\overline N\) is the Satake compactification of a ball quotient. On the other hand it follows from results of Barth and Nieto that \(\overline N\) is also a smooth compactification of a quotient of the Siegel space, so \(N\) is Janus-like. The proof is based on the construction of a suitable branched cover of \(\overline N\) and on results of \textit{B. Hunt}: ``The geometry of some special quotients'', Lect. Notes Math. 1637 (1996; Zbl 0904.14025).