We introduce a variant of global generation for coherent sheaves on abelian varieties which, under certain circumstances, implies ampleness. This extends a criterion of Debarre asserting that a continuously globally generated coherent sheaf on an abelian variety is ample. We apply this to show the ampleness of certain sheaves, which we call naive Fourier-Mukai-Poincar ́e transforms, and to study the structure of GV sheaves. In turn, one of these applications allows to extend the classical existence and connectedness results of Brill-Noether theory to a wider context, e.g. singular curves equipped with a suitable morphism to an abelian variety. Another application is a general inequality of Brill-Noether type involving the Euler characteristic and the homological dimension.
Pareschi, G. (2024). Generation and ampleness of coherent sheaves on abelian varieties, with application to Brill-Noether theory. PURE AND APPLIED MATHEMATICS QUARTERLY, 20(5), 2379-2413 [10.4310/PAMQ.241105233715].
Generation and ampleness of coherent sheaves on abelian varieties, with application to Brill-Noether theory
Giuseppe Pareschi
2024-01-01
Abstract
We introduce a variant of global generation for coherent sheaves on abelian varieties which, under certain circumstances, implies ampleness. This extends a criterion of Debarre asserting that a continuously globally generated coherent sheaf on an abelian variety is ample. We apply this to show the ampleness of certain sheaves, which we call naive Fourier-Mukai-Poincar ́e transforms, and to study the structure of GV sheaves. In turn, one of these applications allows to extend the classical existence and connectedness results of Brill-Noether theory to a wider context, e.g. singular curves equipped with a suitable morphism to an abelian variety. Another application is a general inequality of Brill-Noether type involving the Euler characteristic and the homological dimension.File | Dimensione | Formato | |
---|---|---|---|
pareschi-final-final.pdf
accesso aperto
Tipologia:
Documento in Pre-print
Licenza:
Non specificato
Dimensione
390.66 kB
Formato
Adobe PDF
|
390.66 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.