Jumping Numbers of a Simple Complete Ideal in a Two-dimensional Regular Local Ring

Download or read book Jumping Numbers of a Simple Complete Ideal in a Two-dimensional Regular Local Ring written by Tarmo Järvilehto and published by . This book was released on 2011 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: The multiplier ideals of an ideal in a regular local ring form a family of ideals parameterized by non-negative 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 we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two-dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.