论文标题
计数切线空间的维度到希尔伯特的点计划
Counting Dimensions of Tangent Spaces to Hilbert Schemes of Points
论文作者
论文摘要
在本文中，我们证明了两个结果，这些结果进一步分类了Hilbert方案的平滑度。这是通过计算与单一理想相对应的年轻图表上的箭头类别来完成的，这是基于Jan Cheah在2维情况下显示平滑度的方法的基础。我们证明，就年轻图的几何形状而言，在3个维度和嵌套方案的Hilbert方案上，点在点数的希尔伯特方案上保持平滑状态有足够的条件。特别是，我们证明，当两个图在嵌套方案的点处的两个图之间的区域是矩形时，相应的点是平滑的。我们还证明，如果可以将一个点的三维年轻图定向以使其水平层是矩形的，那么点是光滑的。
In this paper we prove two results which further classify smoothness properties of Hilbert schemes of points. This is done by counting classes of arrows on Young diagrams corresponding to monomial ideals, building on the approach taken by Jan Cheah to show smoothness in the 2 dimensional case. We prove sufficient conditions for points to be smooth on Hilbert schemes of points in 3 dimensions and on nested schemes in 2 dimensions in terms of the geometry of the Young diagram. In particular, we proved that when the region between the two diagrams at a point of the nested scheme is rectangular, the corresponding point is smooth. We also proved that if the three dimensional Young diagram at a point can be oriented such that its horizontal layers are rectangular, then the point is smooth.
