Abstract
Let \(\fancyscript{V}^{r}_{d,g, \delta }\) be the Hilbert scheme of nodal curves in \(\mathbb {P}^r\) 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 \(\fancyscript{V}^{r}_{d,g, \delta }\) having the expected number of moduli.
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Ballico, E., Benzo, L. & Fontanari, C. Families of nodal curves in \(\mathbb {P}^r\) with the expected number of moduli. Boll Unione Mat Ital 7, 183–192 (2014). https://doi.org/10.1007/s40574-014-0009-6
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DOI: https://doi.org/10.1007/s40574-014-0009-6