Effective Hironaka resolution and its Complexity (with appendix on   applications in positive characteristic)
  Building upon works of Hironaka, Bierstone-Milman, Villamayor and Wlodarczyk, we give an a priori estimate for the complexity of the simplified Hironaka algorithm. As a consequence of this result, we show that there exists canonical Hironaka embedded desingularization and principalization over fields of large characteristic (relative to the degrees of generating polynomials). 
Edward Bierstone, Dima Grigoriev, Pierre Milman, Jaroslaw Wlodarczyk
math.AG