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- W3119623203 abstract "Let $mathcal{H}_{d,g,r}$ be the Hilbert scheme parametrizing smooth irreducible and non-degenerate curves of degree $d$ and genus $g$ in $mathbb{P}^r.$ We denote by $mathcal{H}^mathcal{L}_{d,g,r}$ the union of those components of $mathcal{H}_{d,g,r}$ whose general element is linearly normal. In this article we show that $mathcal{H}^mathcal{L}_{d,g,r}$ ($dge g+r-3$) is non-empty in a wider range of triples $(d,g,r)$ beyond the Brill-Noether range. This settles the existence of the Hilbert scheme $mathcal{H}^mathcal{L}_{d,g,r}$ of linearly normal curves in the range $g+r-3le dle g+r$, $rge 3$ with negative Brill-Noether number, which has been left out almost undetermined in some previous works on the subject. We also determine the full range of triples $(d,g,r)$ with $g+r-3le dle g+r$ for which $mathcal{H}^mathcal{L}_{d,g,r}$ is reducible or (irreducible)." @default.
- W3119623203 created "2021-01-18" @default.
- W3119623203 creator A5059793606 @default.
- W3119623203 date "2021-01-03" @default.
- W3119623203 modified "2023-09-27" @default.
- W3119623203 title "Existence and the reducibility of the Hilbert scheme of linearly normal curves in $mathbb{P}^r$ of relatively high degrees" @default.
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