Embedded desingularization of toric varieties

We present a new method to achieve an embedded desingularization of a toric variety. Let $W$ be a regular toric variety defined by a fan $\mathrm{\Sigma }$ and $X\subset W$ be a toric embedding. We construct a finite sequence of combinatorial blowing-ups such that the final strict transforms $X^{\mathrm{\prime }}\subset W^{\mathrm{\prime }}$ are regular and $X^{\mathrm{\prime }}$ has normal crossing with the exceptional divisor.