Embedded desingularization of toric varieties

Abstract

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 $\Sigma$ and $X\subset W$ be a toric embedding. We construct a finite sequence of combinatorial blowing-ups such that the final strict transforms $X^{\prime }\subset W^{\prime }$ are regular and $X^{\prime }$ has normal crossing with the exceptional divisor.

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