Towards the singular locus of the space of arcs
Towards the singular locus of the space of arcs
复制标题
走向弧空间的奇异轨迹
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Ana J. Reguera
中科院分区：
文献类型：
--
作者：
Ana J. Reguera
基于$X_INFTY$的稳定点的有限性，给出了奇异簇$X$的圆弧空间$X_INFTY$的一个理论。我们还展示了如何在这个理论中进行计算。因此，我们得到了从$X_INFTY$的圆弧空间和它的楔形空间(圆弧空间中的圆弧)确定$X$的不变量的过程。更确切地说，我们给出了关于$X_INFTY$的稳定点的正则性的两个概念，并且证明了我们在余维$1$中具有正则性，并且对于曲线的圆弧空间的所有稳定点具有正则性。作为另一个应用，我们给出了从圆弧空间得到的解析分支的Notherian$1$维局部环的具体例子。
We give a theory on the space of arcs $X_infty$ of a singular variety $X$, based on the finiteness property of the stable points of $X_infty$. We also show how computations can be made in this theory. As a consequence, we obtain a process of determining invariants of $X$ from its space of arcs $X_infty$, and from its spaces of wedges (arcs in the space of arcs). More precisely, we give two concepts of regularity for the stable points of $X_infty$, and we show that we have regularity in codimension $1$, and for all stable points of the space of arcs of a curve. As another application, we show concrete examples, obtained from the spaces of arcs, of Noetherian $1$-dimensional local rings which are analytically ramified.