Archivio Istituzionale della RicercaThe purpose of this paper is to study minimal monads associated to a rank two vector bundle ξ± on ππ. In particular, we study situations where ξ± has π»π β(ξ±)=0 for 1<π<πβ1, except for one pair of values (π, π β π). We show that on π8, if π»3 β(ξ±)=π»4 β(ξ±)=0, then ξ± must be decomposable. More generally, we show that for π β©Ύ 4π, there is no indecomposable bundle ξ± for which all intermediate cohomology modules except for π»1 β, π»π β , π»πβπ β , π»πβ1 β are zero.
Rank two bundles on P^n with isolated cohomology / Malaspina, F.; Rao, A. P.. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - 55:5(2023), pp. 2493-2504. [10.1112/blms.12877]
Rank two bundles on P^n with isolated cohomology
Malaspina, F.;
2023
Abstract
The purpose of this paper is to study minimal monads associated to a rank two vector bundle ξ± on ππ. In particular, we study situations where ξ± has π»π β(ξ±)=0 for 1<π<πβ1, except for one pair of values (π, π β π). We show that on π8, if π»3 β(ξ±)=π»4 β(ξ±)=0, then ξ± must be decomposable. More generally, we show that for π β©Ύ 4π, there is no indecomposable bundle ξ± for which all intermediate cohomology modules except for π»1 β, π»π β , π»πβπ β , π»πβ1 β are zero.
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Bulletin of London Math Soc - 2023 - Malaspina - Rank two bundles on Pn mathbf P n with isolated cohomology-2.pdf
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https://hdl.handle.net/11583/2979703