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The purpose of this paper is to study minimal monads associated to a rank two vector bundle  on 𝐏𝑛. In particular, we study situations where  has 𝐻𝑖 βˆ—()=0 for 1<𝑖<π‘›βˆ’1, except for one pair of values (π‘˜, 𝑛 βˆ’ π‘˜). We show that on 𝐏8, if 𝐻3 βˆ—()=𝐻4 βˆ—()=0, then  must be decomposable. More generally, we show that for 𝑛 β©Ύ 4π‘˜, there is no indecomposable bundle  for which all intermediate cohomology modules except for 𝐻1 βˆ—, π»π‘˜ βˆ— , π»π‘›βˆ’π‘˜ βˆ— , π»π‘›βˆ’1 βˆ— 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  on 𝐏𝑛. In particular, we study situations where  has 𝐻𝑖 βˆ—()=0 for 1<𝑖<π‘›βˆ’1, except for one pair of values (π‘˜, 𝑛 βˆ’ π‘˜). We show that on 𝐏8, if 𝐻3 βˆ—()=𝐻4 βˆ—()=0, then  must be decomposable. More generally, we show that for 𝑛 β©Ύ 4π‘˜, there is no indecomposable bundle  for which all intermediate cohomology modules except for 𝐻1 βˆ—, π»π‘˜ βˆ— , π»π‘›βˆ’π‘˜ βˆ— , π»π‘›βˆ’1 βˆ— are zero.
2023
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2979703