Strong resolution of singularities in characteristic zero

Abstract

We present a concise proof for the existence and construction of a strong resolution of excellent schemes of finite type over a field of characteristic zero. Our proof is based on earlier work of Villamayor, Encinas-Villamayor and Bierstone-Milman. It proposes some substantial simplifications which may be helpful for a better understanding of how to prove Hironaka's famous theorem on embedded resolution of singularities.