Families of nodal curves in P^r with the expected number of moduli

Abstract

Let V^{r}_{d,g, \delta} be the Hilbert scheme of nodal curves in P^r of degree d and arithmetic genus g with \delta nodes. Under suitable numerical assumptions on d and g, for every 0 \le \delta \le g we construct an irreducible component of V^{r}_{d,g, \delta} having the expected number of moduli.