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摘要翻译：
在本文中，我们引入了与对$(X,\ba^t)$相关的有理奇点的概念，其中$X$是一个变体，$\ba$是一个理想束，$t$是非负实数。我们证明了大多数关于有理奇点的标准结果都扩展到了这个上下文。我们还证明了一些通常与对数终端对有关的结果在此上下文中具有类似性，包括与附加反演有关的结果。对有理奇点的正特征模拟也被定义和探索。
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英文标题：
《Rational singularities associated to pairs》
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作者：
Karl Schwede and Shunsuke Takagi
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Commutative Algebra 交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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英文摘要：
In this paper we introduce a notion of rational singularities associated to pairs $(X, \ba^t)$ where $X$ is a variety, $\ba$ is an ideal sheaf and $t$ is a nonnegative real number. We prove that most standard results about rational singularities extend to this context. We also show that some results commonly associated with log terminal pairs have analogs in this context, including results related to inversion of adjunction. A positive characteristic analogue of rational singularities of pairs is also defined and explored.
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PDF链接：
https://arxiv.org/pdf/0708.1990
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