# The Stacks Project

## Tag 0BH7

### 80.1. 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 50.1. 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 63.5.1. Similarly for proper morphism, etc, etc.

The code snippet corresponding to this tag is a part of the file spaces-resolve.tex and is located in lines 17–46 (see updates for more information).

\section{Introduction}
\label{section-introduction}

\noindent
This chapter discusses resolution of singularities of
Noetherian algebraic spaces of dimension $2$.
We have already discussed resolution of surfaces
for schemes following Lipman \cite{Lipman} in an earlier
chapter. See
Resolution of Surfaces, Section \ref{resolve-section-introduction}.
Most of the results in this chapter are straightforward
consequences of the results on schemes.

\medskip\noindent
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
\ref{spaces-over-fields-definition-modification}.
Similarly for proper morphism, etc, etc.

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