Irreducibility of the Hilbert scheme of smooth curves in ${\mathbb{P}}^4$ of degree $g+2$ and genus $g$

Changho Keem, Yun-Hwan Kim

We denote by ${\mathcal{H}}_{d,g,r}$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate…