The Full Flag Hilbert Scheme of Nodal Curves and the Punctual Hilbert Scheme of Points of the Cusp Curve

Abstract

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 P¹. Furthermore Hilbert scheme has only one singularty along the punctual one.