Free deformations of hypersurface singularities (Q550580)

\textit{K. Saito} introduced the notion of the so-called Saito free divisors and systems of uniformization equations with respect to them [``On the uniformization of complements of discriminant loci'', RIMS Kokyuroku 287, 117--137 (1977)]. The geometric background of the theory of Saito free divisors and uniformization equations is the theory on versal deformations of isolated hypersurface singularities. The paper is devoted to the study of the classification problem for Saito free divisors, making use of the deformation theory of varieties. An approach for the computation of free deformations of quasicones over quasismooth varieties based on properties of deformations of varieties with \(\mathbb{G}_m\)-action is described. Some applications are discussed, including the problem of compactification of modular spaces and the computation of free deformations for certain simple and unimodal singularities.