Stability and cohomology of kernel bundles on projective space

In this paper, we study the cohomology of vector bundles on projective space defined 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 an asymptotic cohomology vanishing theorem. We characterize the stability of general Steiner bundles on projective space. We also give a criterion for a Steiner bundle to be ample.