On q-Runge domains

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dc.creatorAlaoui, Youssef
dc.date2008-12-26
dc.date.accessioned2026-07-07T12:22:51Z
dc.date.available2026-07-07T12:22:51Z
dc.descriptionIn $[2]$, Coltoiu gave an example of a domain $D\subset\complexes^{6}$ which is 4-complete such that for every ${\mathcal{F}}\in Coh(\complexes^{6})$ the restriction map $H^{3}(\complexes^{6},{\mathcal{F}})\to H^{3}(D,{\mathcal{F}})$ has a dense image but $D$ is not 4-Runge in $\complexes^{6}$. Here, we prove that for every integers $n\geq 4$ and $1\leq q\leq n$ there exists a domain $D\subset \complexes^{n}$ which is not ($\tilde{q}-1$)-Runge in $\complexes^{n}$ but such that for any coherent analytic sheaf ${\mathcal{F}}$ on $\complexes^{n}$ the restriction map $H^{p}(\complexes^{n},{\mathcal{F}})\to H^{3}(D,{\mathcal{F}})$ has a dense image for all $p\geq \tilde{q}-2$ if $q$ does not divide $n$, where $\tilde{q}=n-[\frac{n}{q}]+1$ and $[\frac{n}{q}]$ denotes the integral part of $\frac{n}{q}$.
dc.identifierhttps://arxiv.org/abs/0812.4697
dc.identifierhttp://arxiv.org/abs/0812.4697
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/213796
dc.subjectComplex Variables
dc.subject32E10, 32E40
dc.titleOn q-Runge domains
dc.typetext

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