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Has anyone computed higher Schwarzenberger conditions for vector bundles on projective space, even for rank 2 bundles? Schneider lists them for 2-bundles up to $\mathbb{P}^5$, and for 3-bundles on $\mathbb{P}^3$, but I haven't seen any higher dimensional conditions in the literature. Has anyone computed these, or written a computer program to compute these?

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