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- W2618411607 abstract "Let $mathcal{I}_{d,g,r}$ be the union of irreducible components of the Hilbert scheme whose general points represent smooth irreducible complex curves of degree $d$ and genus $g$ in $mathbb{P}^r$. Severi claimed in [15] that $mathcal{I}_{d,g,r}$ is irreducible if $d geq g+r$. His statement turned out to be correct for $r = 3$ and $4$, while for $r geq 6$, counterexamples have been found by using families of $m$-sheeted covers of rational curves with $m geq 3$. In this work we show the existence of an additional component of $mathcal{I}_{d,g,r}$ whose general elements are double covers of curves of positive genus. In addition, we find upper bounds for the dimension of the possible components of $mathcal{I}_{d,g,r}$." @default.
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- W2618411607 date "2017-05-01" @default.
- W2618411607 modified "2023-09-28" @default.
- W2618411607 title "Reducibility of the Hilbert Scheme of Smooth Curves and Families of Double Covers" @default.
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- W2618411607 doi "https://doi.org/10.11650/tjm/7839" @default.
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