We provide a bound on the Theta-regularity of an arbitrary reduced and irreducible curve embedded in a polarized abelian variety in terms of its degree and codimension. This is an "abelian" version of Gruson-Lazarsfeld-Peskine's bound on the Castelnuovo-Mumford regularity of a non-degenerate curve embedded in a projective space. As an application, we provide a Castelnuovo type bound for the genus of a curve in a (non necessarily principally) polarized abelian variety. Finally, we bound the Theta-regularity of a class of higher dimensional subvarieties in Jacobian varieties, i. e. the Brill-Noether loci associated to a Petri general curve, extending earlier work of Pareschi-Popa.
Theta-regularity of curves and Brill–Noether loci / L. Lombardi, W. Niu. - In: MATHEMATICAL RESEARCH LETTERS. - ISSN 1073-2780. - 23:6(2016), pp. 1761-1787. [10.4310/MRL.2016.v23.n6.a9]
Theta-regularity of curves and Brill–Noether loci
L. Lombardi;
2016
Abstract
We provide a bound on the Theta-regularity of an arbitrary reduced and irreducible curve embedded in a polarized abelian variety in terms of its degree and codimension. This is an "abelian" version of Gruson-Lazarsfeld-Peskine's bound on the Castelnuovo-Mumford regularity of a non-degenerate curve embedded in a projective space. As an application, we provide a Castelnuovo type bound for the genus of a curve in a (non necessarily principally) polarized abelian variety. Finally, we bound the Theta-regularity of a class of higher dimensional subvarieties in Jacobian varieties, i. e. the Brill-Noether loci associated to a Petri general curve, extending earlier work of Pareschi-Popa.File | Dimensione | Formato | |
---|---|---|---|
2) theta-regularity.pdf
accesso riservato
Descrizione: Articolo Principale
Tipologia:
Publisher's version/PDF
Dimensione
228.06 kB
Formato
Adobe PDF
|
228.06 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Theta_regabv6arxiv-1.pdf
accesso aperto
Tipologia:
Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione
389.3 kB
Formato
Adobe PDF
|
389.3 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.