Components of the Hilbert scheme of smooth space curves with the expected number of moduli
Suppose that \(H^3_{d,g}\) is the Hilbert scheme of smooth curves of degree d and genus g in \({\mathbb{P}}^ 3\). If \(g\leq (d^{3/2}/(6\cdot 2^{1/2})+\text{ lower terms}),\) the author constructs a component V of \(H^ 3_{d,g}\) satisfying the following properties: 1. If C is a general curve of V, then \(H^ 1(N_{C/{\mathbb{P}}^ 3})=0\). Hence V is generically smooth and \(\dim (V)=4d.\) 2. The dimension of the image of V in the \(M_ g\), the moduli space of curve, is equal to \(\text{Min}(3g-3,3g-3-(\rho(d,g,3))\). The method of proof is by smoothing reducible nodal curves.
scientific article; zbMATH DE number 4116695