Monomial resolutions of morphisms of algebraic surfaces

Abstract

Suppose that $f:Y\to X$ is a proper, dominant, tamely ramified morphism of algebraic surfaces, over a perfect field. We show that it is possible to perform sequences of monoidal transforms $Y^{\prime }\to Y$ and $X^{\prime }\to X$ to obtain an induced morphism $Y^{\prime }\to Y$ which is a monomial morphism.

25 pages