节曲线的满旗Hilbert格式和尖点曲线的点Hilbert格式
The Full Flag Hilbert Scheme of Nodal Curves and the Punctual Hilbert Scheme of Points of the Cusp Curve
摘要：
本文证明了节线上点的满旗Hilbert格式只有完全相交奇点。研究了尖点曲线上点的Hilbert格式，证明了点Hilbert格式与\mathbb{P}^1是同构的。而且Hilbert格式在点奇点上只有一个奇点。
英文摘要：
In this paper, we show the full flag Hilbert scheme of points of nodal curves has only complete intersection singularities. We study the Hilbert scheme of points of the cusp curve and show the punctual Hilbert scheme is isomorphic to \mathbb{P}^1. Furthermore Hilbert scheme has only one singularty along the punctual one.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
