Free deformations of hypersurface singularities

The article is devoted to the study of the classification problem for Saito free divisors making use of the deformation theory of varieties. In particular, in the quasihomogeneous case, we describe an approach for computation of free deformations of quasicones over quasismooth varieties based on properties of deformations of varieties with $ {mathbb{G}_m} $ -action. We also discuss some applications including the problem of compactification of modular spaces and computation of free deformations for certain simple, unimodal, and unimodular singularities.