The paper investigates vanishing conditions on the intermediate cohomology of a normalized rank $2$ vector bundle $\F$ on $\P^4$ which force $\F$ to split or, at least, to be a non-stable bundle (with few possible exceptions). The results are applied to see when subcanonical surfaces on $\P^4$ are forced to be complete intersections of two hypersurfaces, since subcanonical surfaces are zero loci of non-zero sections of rank $2$ vector bundles.
A few splitting theorems for rank two vector bundles on P^4 / Valabrega, Paolo. - In: ATTI DELLA ACCADEMIA PELORITANA DEI PERICOLANTI, CLASSE DI SCIENZE FISICHE MATEMATICHE E NATURALI. - ISSN 0365-0359. - LXXXIII:(2005).
A few splitting theorems for rank two vector bundles on P^4
VALABREGA, Paolo
2005
Abstract
The paper investigates vanishing conditions on the intermediate cohomology of a normalized rank $2$ vector bundle $\F$ on $\P^4$ which force $\F$ to split or, at least, to be a non-stable bundle (with few possible exceptions). The results are applied to see when subcanonical surfaces on $\P^4$ are forced to be complete intersections of two hypersurfaces, since subcanonical surfaces are zero loci of non-zero sections of rank $2$ vector bundles.Pubblicazioni consigliate
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https://hdl.handle.net/11583/1406873
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