Diagonal Subschemes and Vector Bundles

  title={Diagonal Subschemes and Vector Bundles},
  author={Piotr Pragacz and Vasudevan Srinivas and Vishwambhar Pati},
  journal={Pure and Applied Mathematics Quarterly},
We study when a smooth variety X, embedded diagonally in its Cartesian square, is the zero scheme of a section of a vector bundle of rank dim(X) on X × X. We call this the diagonal property (D). It was known that it holds for all flag manifolds SLn/P . We consider mainly the cases of proper smooth varieties, and the analogous problems for smooth manifolds (“the topological case”). Our main new observation in the case of proper varieties is a relation between (D) and cohomologically trivial line… 

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