Components of the Hilbert Scheme of smooth projective curves using ruled surfaces II: existence of non-reduced components

Youngook Choi, Hristo Iliev, Seonja Kim

For $\gamma \ge 7$ and $g\ge 6\gamma +5$, we construct a family ${\mathcal{F}}^{\prime }$ of curves lying on cones in ${\mathbb{P}}^{g-3\gamma +1}$ over smooth non-degenerate curves of genus $\gamma$ and…