DivisorOnACurve 2001-12-12 17:55:45 2002-09-23 17:05:59 Definition degree curve % 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 {\em divisor} $D$ on a projective nonsingular curve over an algebraically closed field is a formal sum of points $D = \sum n_p p$ where only finitely many of the $n_p\in\mathbb{Z}$ are nonzero. The {\em degree} of a divisor $D$ is ${\rm deg}(D) = \sum n_p$.