Embedded desingularization of toric varieties

We present a new method to achieve an embedded desingularization of a toric variety.Let WW be a regular toric variety defined by a fan ΣΣ and X⊂WX⊂W be a toric embedding. We construct a finite sequence of combinatorial blowing-ups such that the final strict transforms X′⊂W′X′⊂W′ are regular and X′X′ has normal crossing with the exceptional divisor.

► Description of an algorithm of resolution of singularities of toric varieties.
► Resolution is a sequence of blowing up in smooth combinatorial centers.
► Center is given by functions HCodim and E-order.