The reconstruction and recognition problems for homogeneous hypersurface singularities (Q2930207)

\textit{J. N. Mather} and \textit{S. S. T. Yau} [Invent. Math. 69, 243--251 (1982; Zbl 0499.32008)] proved that two complex hypersurface singularities are biholomorphically equivalent if their moduli (Tjurina) algebras are isomorphic. However the proof does not provide an explicit procedure for recovering the singularities from the moduli algebra. In the paper under review, the author surveys the results of the paper [\textit{A. V. Isaev} and \textit{N. G. Kruzhilin}, Proc. Am. Math. Soc. 142, No. 2, 581--590 (2014; Zbl 1305.32016)] which provides an explicit method for reconstructing the singularity from the moduli algebra in case that the singularity is homogeneous. The paper gives an example of the application to the moduli algebra of simple elliptic singularities of type \(\tilde E_7\).NEWLINENEWLINEFor the entire collection see [Zbl 1291.32001].