English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We denote by $\mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves, whichis the union of components whose general point corresponds to a smoothirreducible and non-degenerate curve of degree $d$ and genus $g$ in $\PP^r$. Inthis note, we show that any non-empty $\mathcal{H}_{g+2,g,4}$ is irreduciblewithout any restriction on the genus $g$. Our result augments theirreducibility result obtained earlier by Hristo Iliev(2006), in which severallow genus $g\le 10$ cases have been left untreated.

Irreducibility of the Hilbert scheme of smooth curves in $\Bbb P^4$ of degree $g+2$ and genus $g$