Desingularization of binomial varieties in arbitrary characteristic. Part I. A new resolution function and their properties

In this paper we construct a resolution function that will provide an algorithm of resolution of singularities for binomial ideals, over a field of arbitrary characteristic. For us, a binomial ideal means an ideal generated by binomial equations without any restriction, including monomials and p‐th powers, where p is the characteristic of the base field. This resolution function is based in a modified order function, called E‐order. The E‐order of a binomial ideal is the order of the ideal along a normal crossing divisor E. The resolution function allows us to construct an algorithm of E‐resolution of binomial basic objects, that will be a subroutine of the main resolution algorithm.