Natural Cohomology of General Steiner Bundles
We prove that a general Steiner bundle on projective space over a field of characteris- tic zero has natural cohomology. The proof constructs a matrix of linear forms from multiplication of sections on a curve. When the rank exceeds the dimension of the projective space, a finite étale isogeny of elliptic curves splits the bundles controlling the graded kernels and cokernels into line bundles of equal degree. Choosing the auxiliary line bundle outside a finite set gives maximal rank in every degree. A rational curve provides the boundary case. Two open rank conditions then yield the…
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