projective curve ProjectiveCurve 2002-06-01 09:42:26 2006-09-16 08:39:16 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here A \emph{projective curve} over a field $k$ is an equidimensional projective variety over $k$ of dimension 1. In other \PMlinkescapetext{words}, each of the irreducible components of this variety must have dimension 1.