On rational curves in \(n\)-space with given normal bundle (Q2752203)

Let \(\widetilde S^n_d\) denote the space of unparametrized rational curves of degree \(d\) immersed in \(\mathbb{P}^n\), that is, degree \(d\) immersions \(f:\mathbb{P}' \to\mathbb{P}^n\) modulo \(\mathbb{P}\text{GL}(2)\) actions on \(\mathbb{P}'\). The author gives a stratification of the space \(\widetilde S^n_d\) according to the type of normal bundle of each curve. The strata are than birationally vector bundles over the strata of \(\widetilde S^2_d\). By a result of Kim and Pandharipande \(\widetilde S^2_d\) is known to be rational. The author thereby concludes that all components of the strata of \(\widetilde S^n_d\) which dominate \(\widetilde S^2_d\) are rational.NEWLINENEWLINEFor the entire collection see [Zbl 0966.00024].