# Diagonal Subschemes and Vector Bundles

@article{Pragacz2006DiagonalSA, title={Diagonal Subschemes and Vector Bundles}, author={Piotr Pragacz and Vasudevan Srinivas and Vishwambhar Pati}, journal={Pure and Applied Mathematics Quarterly}, year={2006}, volume={4}, pages={1233-1278} }

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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