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A variety is called $\mathcal D$- affine if the global section functor induces an equivalence between quasi-coherent $\mathcal D$-modules and modules over $\Gamma(X,\mathcal D)$. It is easy to see that affine varieties are $\cal D$-affine. More surprisingly, by an important theorem of Beilinson-Bernstein, (partial) flag varieties are $\mathcal D$-affine as well! So my question is, how rare are $\mathcal D$-affine varieties? Are there other natural examples of $\mathcal D$-affine varieties? |
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Examples for D-affine varieties?A variety is called $\mathcal D$- affine if the global section functor induces an equivalence between $\mathcal D$-modules and modules over $\Gamma(X,\mathcal D)$. It is easy to see that affine varieties are $\cal D$-affine. More surprisingly, by an important theorem of Beilinson-Bernstein, (partial) flag varieties are $\mathcal D$-affine as well! So my question is, how rare are $\mathcal D$-affine varieties? Are there other natural examples of $\mathcal D$-affine varieties?
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