The Stacks project

88.1 Introduction

This chapter discusses resolution of singularities of Noetherian algebraic spaces of dimension $2$. We have already discussed resolution of surfaces for schemes following Lipman [Lipman] in an earlier chapter. See Resolution of Surfaces, Section 54.1. Most of the results in this chapter are straightforward consequences of the results on schemes.

Unless specifically mentioned otherwise all geometric objects in this chapter will be algebraic spaces. Thus if we say “let $f : X \to Y$ be a modification” then this means that $f$ is a morphism as in Spaces over Fields, Definition 71.8.1. Similarly for proper morphism, etc, etc.

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