Embedded resolutions of non necessarily normal affine toric varieties

Abstract

We give a method to construct a partial embedded resolution of a nonnecessarily normal affine toric variety Z(Gamma) equivariantly embedded in a normal affine toric variety Z(rho). This partial resolution is an embedded normalization inside a normal toric ambient space and a resolution of singularities of the ambient space, which always exists, provides an embedded resolution. The advantage is that this partial resolution is completely determined by the embedding Z(Gamma) subset of Z(rho). As a by-product, the construction of the normalization is made without an explicit computation of the saturation of the semigroup Gamma of the toric variety (see [3]). This result is valid for a base field k algebraically closed of arbitrary characteristic.