sentences:  Hironaka's method for arbitrary characteristic varieties gives a resolution method for surfaces, which involves repeatedly blowing up points or smooth curves in the singular set.showed that a surface "Y" (a 2-dimensional reduced Noetherian scheme) has a desingularization if and only if its normalization is finite over "Y" and analytically normal (the completions of its singular points are normal) and has only finitely many singular points.In particular if "Y" is excellent then it has a desingularization.