标题： 关于奇点的喷射闭包 显示英文标题

标题： On jet closures of singularities

摘要： 喷流闭包和喷流支撑闭包最初由de Fernex、Ein和Ishii引入，以解决局部同构问题。 在本文中，我们分别介绍了与喷流闭包和喷流支撑闭包相关的两个局部代数。 我们证明了这两个代数是奇点的不变量。 我们计算并研究了这些不变量在一些有趣的例子中的情况，例如单项式理想和齐次理想的情况。 我们还为喷流闭包引入了一个新的滤过结构和喷流指标。 喷流指标描述了哪个喷流方案能够恢复基方案的信息。 此外，我们获得了一些喷流指标的性质。 关键词：喷流闭包，喷流支撑闭包和滤过结构。 显示英文摘要

摘要： The jet closure and jet support closure were first introduced by de Fernex, Ein and Ishii to solve the local isomorphism problem. In this paper, we introduce two local algebras associated to jet closure and jet support closure respectively. We show that these two algebras are invariants of the singularities. We compute and investigate these invariants for some interesting cases, such as the cases of monomial ideals and homogeneous ideals. We also introduce a new filtration and jet index to jet closures. The jet index describes which jet scheme recover the information of base scheme. Moreover, we obtain some properties of the jet index. Keywords:jet closure, jet support closure and filtration.