Let $mathcal{I}_{d,g,R}$ be the union of irreducible components of the Hilbert scheme whose general points parametrize smooth, irreducible, curves of degree $d$, genus $g$, which are non--degenerate in the projective space $mathbb{P}^R$. Under some numerical assumptions on $d$, $g$ and $R$, we construct irreducible components of $mathcal{I}_{d,g,R}$ other than the so-called {em distinguished component}, dominating the moduli space $mathcal{M}_g$ of smooth genus--$g$ curves, which are generically smooth and turn out to be of dimension higher than the expected one. The general point of any such a component corresponds to a curve $X subset mathbb{P}^R$ which is a suitable ramified $m$--cover of an irrational curve $Y subset mathbb{P}^{R-1}$, $m geqslant 2$, lying in a surface cone over $Y$. extends some of the results in previous papers of Y. Choi, H. Iliev, S. Kim (cf. [12,13] in Bibliography).

Flamini, F., Supino, P. (2021). On some components of Hilbert schemes of curves.

On some components of Hilbert schemes of curves

Paola Supino
2021

Abstract

Let $mathcal{I}_{d,g,R}$ be the union of irreducible components of the Hilbert scheme whose general points parametrize smooth, irreducible, curves of degree $d$, genus $g$, which are non--degenerate in the projective space $mathbb{P}^R$. Under some numerical assumptions on $d$, $g$ and $R$, we construct irreducible components of $mathcal{I}_{d,g,R}$ other than the so-called {em distinguished component}, dominating the moduli space $mathcal{M}_g$ of smooth genus--$g$ curves, which are generically smooth and turn out to be of dimension higher than the expected one. The general point of any such a component corresponds to a curve $X subset mathbb{P}^R$ which is a suitable ramified $m$--cover of an irrational curve $Y subset mathbb{P}^{R-1}$, $m geqslant 2$, lying in a surface cone over $Y$. extends some of the results in previous papers of Y. Choi, H. Iliev, S. Kim (cf. [12,13] in Bibliography).
Flamini, F., Supino, P. (2021). On some components of Hilbert schemes of curves.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/378370
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