Memoirs of the American Mathematical Society 2011; 78 pp; softcover Volume: 214 ISBN10: 0821848119 ISBN13: 9780821848111 List Price: US$70 Individual Members: US$42 Institutional Members: US$56 Order Code: MEMO/214/1009
 The multiplier ideals of an ideal in a regular local ring form a family of ideals parameterized by nonnegative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript the author gives an explicit formula for the jumping numbers of a simple complete ideal in a twodimensional regular local ring. In particular, he obtains a formula for the jumping numbers of an analytically irreducible plane curve. He then shows that the jumping numbers determine the equisingularity class of the curve. Table of Contents  Introduction
 Preliminaries on complete ideals
 Arithmetic of the point basis
 The dual graph
 Multiplier ideals and jumping numbers
 Main theorem
 Proof of main theorem
 Jumping numbers of a simple ideal
 Jumping numbers of an analytically irreducible plane curve
 Bibliography
