Abstract
We compute the global dimension of the twisted rings of global differential operators Dλ on complex projective n-space. As λ varies through the complex numbers, this global dimension takes on the values n, 2n and infinity. We also study the embedding of Dλ in the Weyl algebra An in the cases when the global dimension is infinite. In these cases, we see that the flat dimension of An as a Dλ-module is infinite as well.
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