论文标题
嵌入弧空空间
Embedding codimension of the space of arcs
论文作者
论文摘要
我们介绍了一个任意局部环的嵌入编码，建立一些一般属性的概念，并详细研究有限类型方案的弧空空间。将嵌入嵌入的编码视为奇异性的衡量标准，我们的主要结果可以解释为说弧空空间的奇异性在弧线上是最大的，这些弧完全嵌入了基础方案的奇异基因座，并且随着我们离开所述景点而逐渐改善。 As an application, we complement a theorem of Drinfeld, Grinberg, and Kazhdan on formal neighborhoods in arc spaces by providing a converse to their theorem, an optimal bound for the embedding codimension of the formal model appearing in the statement, a precise formula for the embedding dimension of the model constructed in Drinfeld's proof, and a geometric meaningful way of realizing the decomposition stated in the定理。
We introduce a notion of embedding codimension of an arbitrary local ring, establish some general properties, and study in detail the case of arc spaces of schemes of finite type over a field. Viewing the embedding codimension as a measure of singularities, our main result can be interpreted as saying that the singularities of the arc space are maximal at the arcs that are fully embedded in the singular locus of the underlying scheme, and progressively improve as we move away from said locus. As an application, we complement a theorem of Drinfeld, Grinberg, and Kazhdan on formal neighborhoods in arc spaces by providing a converse to their theorem, an optimal bound for the embedding codimension of the formal model appearing in the statement, a precise formula for the embedding dimension of the model constructed in Drinfeld's proof, and a geometric meaningful way of realizing the decomposition stated in the theorem.
