Let (Formula presented.) be a quotient of a bounded domain in (Formula presented.). Under suitable assumptions, we prove that every subvariety of (Formula presented.) not included in the branch locus of the quotient map is of log-general type in some orbifold sense. This generalizes a recent result by Boucksom and Diverio, which treated the case of compact, étale quotients. Finally, in the case where (Formula presented.) is compact, we give a sufficient condition under which there exists a proper analytic subset of (Formula presented.) containing all entire curves and all subvarieties not of general type (meant this time in in the usual sense as opposed to the orbifold sense).

On subvarieties of singular quotients of bounded domains / Cadorel, B.; Diverio, S.; Guenancia, H.. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - (2022). [10.1112/jlms.12660]

On subvarieties of singular quotients of bounded domains

Diverio S.;
2022

Abstract

Let (Formula presented.) be a quotient of a bounded domain in (Formula presented.). Under suitable assumptions, we prove that every subvariety of (Formula presented.) not included in the branch locus of the quotient map is of log-general type in some orbifold sense. This generalizes a recent result by Boucksom and Diverio, which treated the case of compact, étale quotients. Finally, in the case where (Formula presented.) is compact, we give a sufficient condition under which there exists a proper analytic subset of (Formula presented.) containing all entire curves and all subvarieties not of general type (meant this time in in the usual sense as opposed to the orbifold sense).
2022
Logarithmic variants of Lang’s conjecture; quotients of bounded domains; varieties and orbifolds of log-general type; Bergman metric; L2-estimates for ∂ ̄-equation
01 Pubblicazione su rivista::01a Articolo in rivista
On subvarieties of singular quotients of bounded domains / Cadorel, B.; Diverio, S.; Guenancia, H.. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - (2022). [10.1112/jlms.12660]
File allegati a questo prodotto
File Dimensione Formato  
Cadorel_On subvarieties_2022.pdf

accesso aperto

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Creative commons
Dimensione 397.05 kB
Formato Adobe PDF
397.05 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1656175
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 0
social impact