Explicit structures of three-dimensional hypersurface purely elliptic singularities of type \((0,1)\) (Q5949476)

Let \((X,x)\) be an isolated normal Gorenstein singularity of dimension \(\geq 2\). The singularity is called purely elliptic if \(\delta_m(X,x) = 1\) for all \(m\). Purely elliptic hypersurface singularities with non-degenerate Newton boundary are studied using toric geometry. If their Newton boundary \(\Gamma(f)\) is non-degenerate, they can be characterised by the property \((1, \dots, 1) \in \Gamma(f)\) [cf. \textit{K. Watanabe}, Adv. Stud. Pure Math. 8, 671-685 (1987; Zbl 0659.32015)]. Purely elliptic singularities are classified by means of the mixed Hodge structure of the cohomology of the exceptional set in the resolution into types \((0,0), \dots, (0,n-1)\), if \(n\) is the dimension. After collecting some general results, the author studies especially 3-dimensional purely elliptic singularities of type \((0,1)\).