论文标题
守时两个方面的守时细胞二维
Gröbner cells of punctual Hilbert schemes in dimension two
论文作者
论文摘要
我们从关于格布纳细胞的常规二维局部环的守时希尔伯特方案的全面讨论开始。这些方案是Grothendieck-Deligne Norm Map（Hilbert-Chow Morphism）中最简单的纤维，在对光滑表面希尔伯特方案的研究中起着重要作用。它们通常是奇异的，但是他们的gröbner细胞是仿射空间。他们承认由于浓汤和瓦拉而引起的明确参数化。我们使用它来获得平面曲线奇点压实的雅各布人的gröbner分解，即使对于广义的雅各布人来说，这也是不平凡的（仅主要理想）。其中之一是压实雅各布人的某些变体的拓扑不变性和用于准耶和华平面曲线奇异性和一些类似家庭的分析变形的相应动机性超级物质。
We begin with a comprehensive discussion of the punctual Hilbert scheme of the regular two-dimensional local ring in terms of the Gröbner cells. These schemes are the most degenerate fibers of the Grothendieck-Deligne norm map (the Hilbert-Chow morphism), playing an important role in the study of Hilbert schemes of smooth surfaces. They are generally singular, but their Gröbner cells are affine spaces; they admit an explicit parametrization due to Conca and Valla. We use this to obtain the Gröbner decomposition of compactified Jacobians of plane curve singularities, which is non-trivial even for the generalized Jacobians (principal ideals only). One of the application is the topological invariance of certain variants of compactified Jacobians and the corresponding motivic superpolynomials for analytic deformations of quasi-homogenous plane curve singularities and some similar families.
