关于参数化曲线奇异性的Delta
On Delta for parameterized Curve Singularities
摘要：
我们考虑家庭的参数化约化曲线奇点的诺特基计划，并证明了三角洲不变是连续的。在我们的设置中，家庭中的每个曲线奇点是一个参数化的图像，而不是一个态射的纤维。这个问题出现在与右左分类的参数化曲线奇点定义在一个领域的积极特征。我们证明了一个参数化的左右决定性的δ和连续性定理提供了一个家庭中的决定性的同时界。事实上，底空间可以是一个任意的诺特计划造成一些困难，但（不仅）感兴趣的计算目的。
英文摘要：
We consider families of parameterizations of reduced curve singularities over a Noetherian base scheme and prove that the delta invariant is semicontinuous. In our setting, each curve singularity in the family is the image of a parameterization and not the fiber of a morphism. The problem came up in connection with the right-left classification of parameterizations of curve singularities defined over a field of positive characteristic. We prove a bound for right-left determinacy of a parameterization in terms of delta and the semicontinuity theorem provides a simultaneous bound for the determinacy in a family. The fact that the base space can be an arbitrary Noetherian scheme causes some difficulties but is (not only) of interest for computational purposes.
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