Desingularization of binomial varieties in arbitrary characteristic. Part II. Combinatorial desingularization algorithm

In this paper we construct a combinatorial algorithm of resolution of singularities for binomial ideals, over a field of arbitrary characteristic. This algorithm is applied to any binomial ideal. This means ideals generated by binomial equations without any restriction, including monomials and $p$-th powers, where $p$ is the characteristic of the base field. In particular, this algorithm works for toric ideals. However, toric geometry tools are not needed, the algorithm is constructed following the same point of view as Villamayor algorithm of resolution of singularities in characteristic zero.