Tsuchihashi's cusp singularities and automorphisms of Hilbert modular variety cusps (Q1065097)

\textit{H. Tsuchihashi} [Tôhoku J. Math., II. Ser. 35, 607--639 (1983; Zbl 0585.14004)] introduced a class of cusp singularities extending the class of Hilbert modular variety cusps. Here, a necessary and sufficient condition for a cusp in this sense to be a Hilbert modular variety cusp is proved. Some cusps occur as finite quotients of Hilbert modular variety cusps: these are described, and so, more generally, are all the germs of automorphisms at a Hilbert modular variety cusp.