A remark on the Hilbert scheme of smooth complex space curves (Q1814203)

The author shows that the Hilbert scheme \({\mathcal I}'_{d,g,3}\) of smooth, complex, curves of degree \(d\) and genus \(g\) in \(\mathbb{P}^ 3\) is irreducible when \(d=11\), \(g=10\) and when \(d=10\), \(g=9\). Then, by using results of a previous paper in cooperation with \textit{Seon Ja Kim} [J. Algebra 145, 240-248 (1992)], he proves that \({\mathcal I}'_{d,g,3}\) is irreducible for all \(d\) and \(g\) such that \(d>g\) and positive \(\rho(d,g,3)\) (the Brill-Noether number). Some results by \textit{M. Coppens} [Ann. Mat. Pura Appl., IV. Ser. 157, 183-197 (1990; Zbl 0742.14025)] are also used.