Mathematics

Given a hypersurface X along with a suitable action of a cyclic group of r-th-roots of unity G on X, a hypersurface singularity P in X can be regarded as hyperquotient singularity Q in the quotient space Y=X/G. The goal of this talk is to understand the nature of such singularities, i.e. canonical or terminal, etc.  In particular, we will establish the fact that such information is encoded in some combinatorial data associated with the group G and newton polyhedron of the polynomial f which defines X.