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In this paper, we study the cohomology of vector bundles on projective spacedefined as kernels or cokernels of general maps $V_1 \to V_2$, where the $V_i$are direct sums of line bundles or certain exceptional bundles. We prove anasymptotic cohomology vanishing theorem. We characterize the stability ofgeneral Steiner bundles on projective space. We also give a criterion for aSteiner bundle to be ample.

Stability and cohomology of kernel bundles on projective space