Deformations of three dimensional cusp singularities (Q1123935)

The author continues his investigation of cusp singularities [ibid. 35, 607-639 (1983; Zbl 0585.14004)]. This time he studies deformations of 3- dimensional cusp singularities (V,p), which are not of Hilbert modular type. [The Hilbert modular cusp singularities in dimension 3 or more are rigid, see \textit{E. Freitag} and \textit{R. Kiehl}, Invent. Math. 24, 121-148 (1974; Zbl 0304.32018).] Using toric variety techniques, the author constructs an open cover of the exceptional (toric) divisor of a resolution of (V,p). Using this, a deformation of the resolution is obtained, which contracts to a deformation of (V,p). This family is actually the versal family, proving that these cusp singularities are unobstructed and non-smoothable. A preceding group cohomology computation implies that they are not taut.