标题： 跳跃数在有理奇点的代数曲面上 显示英文标题

标题： Jumping Numbers on Algebraic Surfaces with Rational Singularities

摘要： 在本文中，我们研究复代数曲面上有理奇点处理想的相关跳跃数。 通过理解在固定解消上约化除子的贡献，我们能够提出一个算法来寻找理想的相关跳跃数。 这特别展示了如何从其最小解消的数值数据计算平面曲线的相关跳跃数。 此外，计算了杜瓦尔或环面奇点处奇异点上极大理想的相关跳跃数，并探讨了在光滑情况下的应用。 显示英文摘要

摘要： In this article, we study the jumping numbers of an ideal in the local ring at rational singularity on a complex algebraic surface. By understanding the contributions of reduced divisors on a fixed resolution, we are able to present an algorithm for finding of the jumping numbers of the ideal. This shows, in particular, how to compute the jumping numbers of a plane curve from the numerical data of its minimal resolution. In addition, the jumping numbers of the maximal ideal at the singular point in a Du Val or toric surface singularity are computed, and applications to the smooth case are explored.