Constructing overweight deformations using polyhedra.

 I will discuss the following question: Given an irreducible affine hypersurface singularity $ X = V(f) $, is it possible to find a re-embedding into a possibly larger regular ambient space $ Z $ such that, in there, $ X $ can be considered as an overweight deformation of a (not necessarily normal) toric variety $ Y $? When this is possible, one can deduce crucial information on $ X $ by studying $ Y $, e.g. a resolution of singularities of $ Y $ is also one for $ X $. I will explain the ideas how such a re-embedding can be achieved by using weighted polyhedra in particular cases. This is joint work with Hussein Mourtada.