Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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
MathSciNet review: 1221729
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14M15, 58F25

Retrieve articles in all journals with MSC: 14M15, 58F25

Additional Information

PII: S 0002-9939(1995)1221729-X
Article copyright: © Copyright 1995 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia