The Riccati flow and singularities of Schubert varieties

Author:
James S. Wolper

Journal:
Proc. Amer. Math. Soc. **123** (1995), 703-709

MSC:
Primary 14M15; Secondary 58F25

DOI:
https://doi.org/10.1090/S0002-9939-1995-1221729-X

MathSciNet review:
1221729

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the Grassmannian of *m*-dimensional subspaces of an *n*-dimensional *k*-vector space, with or **C**. Fix an matrix *R* with coefficients in *k*. The Riccati Flow on is the action of a one-parameter subgroup of , given by . We prove:

**Theorem**. *Let X be a Schubert variety in* . *Then there exists a Riccati flow* *on X and a stable manifold W for* *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*.

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DOI:
https://doi.org/10.1090/S0002-9939-1995-1221729-X

Article copyright:
© Copyright 1995
American Mathematical Society