The present paper concerns the invariants of generically nef vector bundles on ruled surfaces. By Mehta–Ramanathan Restriction Theorem and by Miyaoka characterization of semistable vector bundles on a curve, the generic nefness can be considered as a weak form of semista- bility. We establish a Bogomolov-type inequality for generically nef vector bundles with nef general fiber restriction on ruled surfaces with no negative section, see Theorem 3.1. This gives an affirmative answer in this case to a problem posed by Peternell [17]. Concerning ruled surfaces with a negative section, we prove a similar result for generically nef vector bundles, with nef and balanced general fiber restriction and with a numerical condition on first Chern class, which is satisfied, for instance, if in its class there is a reduced divisor, see Theorem 3.5. Finally, we use such results to bound the invariants of curve fibrations, which factor through finite covers of ruled surfaces.
Generically nef vector bundles on ruled surfaces
Valentina, Beorchia
;
2019-01-01
Abstract
The present paper concerns the invariants of generically nef vector bundles on ruled surfaces. By Mehta–Ramanathan Restriction Theorem and by Miyaoka characterization of semistable vector bundles on a curve, the generic nefness can be considered as a weak form of semista- bility. We establish a Bogomolov-type inequality for generically nef vector bundles with nef general fiber restriction on ruled surfaces with no negative section, see Theorem 3.1. This gives an affirmative answer in this case to a problem posed by Peternell [17]. Concerning ruled surfaces with a negative section, we prove a similar result for generically nef vector bundles, with nef and balanced general fiber restriction and with a numerical condition on first Chern class, which is satisfied, for instance, if in its class there is a reduced divisor, see Theorem 3.5. Finally, we use such results to bound the invariants of curve fibrations, which factor through finite covers of ruled surfaces.File | Dimensione | Formato | |
---|---|---|---|
Valentina-Francesco2019_Article_GenericallyNefVectorBundlesOnR.pdf
Accesso chiuso
Tipologia:
Documento in Versione Editoriale
Licenza:
Copyright Editore
Dimensione
532.76 kB
Formato
Adobe PDF
|
532.76 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
2928310_Valentina-Francesco2019_Article_GenericallyNefVectorBundlesOnR-PostPrint.pdf
accesso aperto
Descrizione: Post Print VQR3
Tipologia:
Bozza finale post-referaggio (post-print)
Licenza:
Digital Rights Management non definito
Dimensione
860.15 kB
Formato
Adobe PDF
|
860.15 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.