Abstract
Abstract Here we study vector bundles E on the Hirzebruch surface F e such that their twists by a spanned, but not ample, line bundle M = $$ \mathcal{O} $$ Fe(h + ef) have natural cohomology, i.e. h 0(F e, E(tM)) > 0 implies h 1(F e, E(tM)) = 0.
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