Abstract
Let Q be a smooth quadric surface and E a vector bundle on Q. We say that E is weakly line positive if for each line T ⊂ Q the bundle E|T is a direct sum of line bundles of degree ≥ 0. Here we classify the quadruples (a,b,u,v) ∈ Z 4 such that there is a weakly line positive extension of OQ(a,b)
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