On the canonical degrees of curves in varieties of general type
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AUTISSIER, Pascal | |
| hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
| dc.contributor.author | CHAMBERT-LOIR, Antoine | |
| hal.structure.identifier | Institut de Recherche Mathématique Avancée [IRMA] | |
| dc.contributor.author | GASBARRI, Carlo | |
| dc.date.accessioned | 2024-04-04T02:26:56Z | |
| dc.date.available | 2024-04-04T02:26:56Z | |
| dc.date.created | 2010-03-19 | |
| dc.date.issued | 2012 | |
| dc.identifier.issn | 1016-443X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189994 | |
| dc.description.abstractEn | A widely believed conjecture predicts that curves of bounded geometric genus lying on a variety of general type form a bounded family. One may even ask whether the canonical degree of a curve $C$ in a variety of general type is bounded from above by some expression $a\chi(C)+b$, where $a$ and $b$ are positive constants, with the possible exceptions corresponding to curves lying in a strict closed subset (depending on $a$ and $b$). A theorem of Miyaoka proves this for smooth curves in minimal surfaces, with $a>3/2$. A conjecture of Vojta claims in essence that any constant $a>1$ is possible provided one restricts oneself to curves of bounded gonality. We show by explicit examples that in general, the constant $a$ has to be at least equal to the dimension of the ambient variety. | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.title.en | On the canonical degrees of curves in varieties of general type | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00039-012-0188-1 | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| dc.identifier.arxiv | 1003.3804 | |
| bordeaux.journal | Geometric And Functional Analysis | |
| bordeaux.page | 1051-1061 | |
| bordeaux.volume | 22 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 5 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00600376 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00600376v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Geometric%20And%20Functional%20Analysis&rft.date=2012&rft.volume=22&rft.issue=5&rft.spage=1051-1061&rft.epage=1051-1061&rft.eissn=1016-443X&rft.issn=1016-443X&rft.au=AUTISSIER,%20Pascal&CHAMBERT-LOIR,%20Antoine&GASBARRI,%20Carlo&rft.genre=article |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||