## 53.1 Introduction

In this chapter we develop some of the theory of algebraic curves. A reference covering algebraic curves over the complex numbers is the book [ACGH].

What we already know. Besides general algebraic geometry, we have already proved some specific results on algebraic curves. Here is a list.

1. We have discussed affine opens of and ample invertible sheaves on $1$ dimensional Noetherian schemes in Varieties, Section 33.38.

2. We have seen a curve is either affine or projective in Varieties, Section 33.43.

3. We have discussed degrees of locally free modules on proper curves in Varieties, Section 33.44.

4. We have discussed the Picard scheme of a nonsingular projective curve over an algebraically closed field in Picard Schemes of Curves, Section 44.1.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).