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

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

2009-06-17

arxiv.org/abs/0906.3097v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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