DESINGULARIZATION OF BINOMIAL VARIETIES IN ARBITRARY CHARACTERISTIC. PART II: COMBINATORIAL DESINGULARIZATION ALGORITHM

摘要

In this paper, we construct a combinatorial algorithm of resolution of singularities for binomial ideals, over a field of arbitrary characteristic. This algorithm can be applied to any binomial ideal. This means ideals generated by binomial equations without any restriction, including monomials and pth 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, and the algorithm is constructed following the same point of view as the Villamayor algorithm of resolution of singularities in characteristic zero.