论文标题
希尔伯特·盖特（Galois）封闭和基本组成部分
Galois closures and elementary components of Hilbert schemes of points
论文作者
论文摘要
巴尔加瓦（Bhargava）和本文的头号作者提出了一个功能性的galois封闭操作，用于有限级环扩展，并概括了grothendieck和katz-mazur的构造。在本文中，我们概括了Galois的关闭，并将其应用于Hilbert Hilbert方案的新型无限元素。我们表明，这些组件是基本的，从某种意义上说，它们在某个点上支持代数。此外，我们通过合适的Socle元素改装从Galois封闭获得的基本组成部分的二级家庭。
Bhargava and the first-named author of this paper introduced a functorial Galois closure operation for finite-rank ring extensions, generalizing constructions of Grothendieck and Katz--Mazur. In this paper, we generalize Galois closures and apply them to construct a new infinite family of irreducible components of Hilbert schemes of points. We show that these components are elementary, in the sense that they parametrize algebras supported at a point. Furthermore, we produce secondary families of elementary components obtained from Galois closures by modding out by suitable socle elements.
