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- W4236033207 abstract "Let $operatorname {Gr}(m,n)$ be the Grassmannian of m-dimensional subspaces of an n-dimensional k-vector space, with $k = {mathbf {R}}$ or C. Fix an $n times n$ matrix R with coefficients in k. The Riccati Flow $Phi$ on $operatorname {Gr}(m,n)$ is the action of a one-parameter subgroup of ${text {GL}_n}(k)$, given by ${Phi _t}(Lambda ) = {e^{Rt}}Lambda$. We prove: Theorem. Let X be a Schubert variety in $operatorname {Gr}(m,n)$. Then there exists a Riccati flow $Phi$ on X and a stable manifold W for $Phi$ such that W is the smooth locus of X. Corollary (over C). X as above is smooth if and only if the cohomology of X satisfies Poincaré Duality." @default.
- W4236033207 created "2022-05-12" @default.
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- W4236033207 date "1995-03-01" @default.
- W4236033207 modified "2023-10-16" @default.
- W4236033207 title "The Riccati Flow and Singularities of Schubert Varieties" @default.
- W4236033207 doi "https://doi.org/10.2307/2160788" @default.
- W4236033207 hasPublicationYear "1995" @default.
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