Let π: X → ℙn−1 be an elliptic fibration obtained by resolving the indeterminacy of the projection of a cubic hypersurface Y of ℙn+1 from a line L not contained in Y . We prove that the Mordell-Weil group of π is finite if and only if the Cox ring of X is finitely generated. We also provide a presentation of the Cox ring of X when it is finitely generated.

Hausen, J., Laface, A., Tironi, A., Ugaglia, L. (2016). On cubic elliptic varieties. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 368(1), 689-708 [10.1090/tran/6353].

On cubic elliptic varieties

UGAGLIA, Luca
2016-01-01

Abstract

Let π: X → ℙn−1 be an elliptic fibration obtained by resolving the indeterminacy of the projection of a cubic hypersurface Y of ℙn+1 from a line L not contained in Y . We prove that the Mordell-Weil group of π is finite if and only if the Cox ring of X is finitely generated. We also provide a presentation of the Cox ring of X when it is finitely generated.
2016
Settore MAT/03 - Geometria
Hausen, J., Laface, A., Tironi, A., Ugaglia, L. (2016). On cubic elliptic varieties. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 368(1), 689-708 [10.1090/tran/6353].
File in questo prodotto:
File Dimensione Formato  
tran6353.pdf

Solo gestori archvio

Descrizione: Articolo principale
Tipologia: Versione Editoriale
Dimensione 315.44 kB
Formato Adobe PDF
315.44 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
200793_Ugaglia_ON CUBIC ELLIPTIC VARIETIES.pdf

accesso aperto

Tipologia: Post-print
Dimensione 480.95 kB
Formato Adobe PDF
480.95 kB Adobe PDF Visualizza/Apri

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/10447/200793
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact