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Hartogs-type theorems in real algebraic geometry, II

2024
journal article
article
10.1007/s00208-023-02734-3
Journal
Mathematische Annalen
200
Author
Bilski Marcin

Bochnak Jacek

Kucharz Wojciech
Volume
389
Number
4
Pages
3747-3768
ISSN
0025-5831
eISSN
1432-1807
URL
https://link.springer.com/article/10.1007/s00208-023-02734-3
Access date
2024-07-03
Language
English
Journal language
English
Abstract in English

Let be a function defined on a connected nonsingular real algebraic set in with . We prove that f is a regular function whenever the restriction is a regular function for every algebraic curve in that is an analytic submanifold homeomorphic to the unit circle and has at most one singular point. We also have a suitable version of this result for not necessarily connected.

Affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.abstract.enLet $f:X\rightarrow \mathbb{R}$ be a function defined on a connected nonsingular real algebraic set $X$ in $\mathbb{R}^{2}$ with $dimX \geq 2$ . We prove that f is a regular function whenever the restriction $f\mid_{c}$ is a regular function for every algebraic curve $C$ in $X$ that is an analytic submanifold homeomorphic to the unit circle and has at most one singular point. We also have a suitable version of this result for $X$ not necessarily connected.
dc.affiliationWydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.authorBilski, Marcin - 127343
dc.contributor.authorBochnak, Jacek
dc.contributor.authorKucharz, Wojciech - 200567
dc.date.accession2024-07-03
dc.date.accessioned2024-07-03T08:49:11Z
dc.date.available2024-07-03T08:49:11Z
dc.date.issued2024
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.number4
dc.description.physical3747-3768
dc.description.versionostateczna wersja wydawcy
dc.description.volume389
dc.identifier.doi10.1007/s00208-023-02734-3
dc.identifier.eissn1432-1807
dc.identifier.issn0025-5831
dc.identifier.urihttps://ruj.uj.edu.pl/handle/item/367486
dc.identifier.weblinkhttps://link.springer.com/article/10.1007/s00208-023-02734-3
dc.languageeng
dc.language.containereng
dc.rightsUdzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa
dc.rights.licenceCC-BY
dc.rights.simpleviewWolny dostęp
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/legalcode.pl
dc.share.typeinne
dc.source.integratorfalse
dc.subtypeArticle
dc.titleHartogs-type theorems in real algebraic geometry, II
dc.title.journalMathematische Annalen
dc.typeJournalArticle
dspace.entity.typePublicationen
dc.abstract.en
Let $f:X\rightarrow \mathbb{R}$ be a function defined on a connected nonsingular real algebraic set $X$ in $\mathbb{R}^{2}$ with $dimX \geq 2$ . We prove that f is a regular function whenever the restriction $f\mid_{c}$ is a regular function for every algebraic curve $C$ in $X$ that is an analytic submanifold homeomorphic to the unit circle and has at most one singular point. We also have a suitable version of this result for $X$ not necessarily connected.
dc.affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.author
Bilski, Marcin - 127343
dc.contributor.author
Bochnak, Jacek
dc.contributor.author
Kucharz, Wojciech - 200567
dc.date.accession
2024-07-03
dc.date.accessioned
2024-07-03T08:49:11Z
dc.date.available
2024-07-03T08:49:11Z
dc.date.issued
2024
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.number
4
dc.description.physical
3747-3768
dc.description.version
ostateczna wersja wydawcy
dc.description.volume
389
dc.identifier.doi
10.1007/s00208-023-02734-3
dc.identifier.eissn
1432-1807
dc.identifier.issn
0025-5831
dc.identifier.uri
https://ruj.uj.edu.pl/handle/item/367486
dc.identifier.weblink
https://link.springer.com/article/10.1007/s00208-023-02734-3
dc.language
eng
dc.language.container
eng
dc.rights
Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa
dc.rights.licence
CC-BY
dc.rights.simpleview
Wolny dostęp
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/legalcode.pl
dc.share.type
inne
dc.source.integrator
false
dc.subtype
Article
dc.title
Hartogs-type theorems in real algebraic geometry, II
dc.title.journal
Mathematische Annalen
dc.type
JournalArticle
dspace.entity.typeen
Publication
Affiliations
Wydział Matematyki i Informatyki
Bilski, Marcin
mathematics
Kucharz, Wojciech
mathematics
No affiliation
Bochnak, Jacek

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