Rank two bundles on P^n with isolated cohomology

The purpose of this paper is to study minimal mon- ads associated to a rank two vector bundle  on 𝐏𝑛. In particular, we study situations where  has 𝐻 𝑖 ∗ () = 0 for 1 < 𝑖 < 𝑛 − 1, except for one pair of values (𝑘, 𝑛 − 𝑘). We show that on 𝐏8, if 𝐻 3 ∗ () = 𝐻 4 ∗ () = 0, then  must be decomposable. More generally, we show that for 𝑛 ⩾ 4𝑘, there is no indecomposable bundle  for which all intermediate cohomology modules except for 𝐻 1 ∗ , 𝐻 𝑘 ∗ , 𝐻 𝑛−𝑘 ∗ , 𝐻 𝑛−1 ∗ are zero. M S C 2 0 2 0 14F06, 14J60 (primary)