Archivio Istituzionale della RicercaThe paper investigates vanishing conditions on the first cohomology module of a normalized rank $2$ vector bundle $\shE$ on $\PP^3$ which force $\shE$ to split, and finds therefore strategic levels of non-vanishing for a non-split bundle. The present conditions improve other conditions known in the literature and are obtained with simple computations on the Euler characteristic function, avoiding the speciality lemma, Barth's restriction theorem, the discriminat property, and other heavy tools.
NON-VANISHING THEOREMS FOR NON-SPLIT RANK 2 Vector Bundles on P3:a Simple Approach, Atti / Valabrega, Paolo. - In: ATTI DELLA ACCADEMIA PELORITANA DEI PERICOLANTI, CLASSE DI SCIENZE FISICHE MATEMATICHE E NATURALI. - ISSN 0365-0359. - LXXXVII:(2009).
NON-VANISHING THEOREMS FOR NON-SPLIT RANK 2 Vector Bundles on P3:a Simple Approach, Atti
VALABREGA, Paolo
2009
Abstract
The paper investigates vanishing conditions on the first cohomology module of a normalized rank $2$ vector bundle $\shE$ on $\PP^3$ which force $\shE$ to split, and finds therefore strategic levels of non-vanishing for a non-split bundle. The present conditions improve other conditions known in the literature and are obtained with simple computations on the Euler characteristic function, avoiding the speciality lemma, Barth's restriction theorem, the discriminat property, and other heavy tools.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11583/1916300
Attenzione
Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo