Rigidity of smooth Schubert varieties in Hermitian symmetric spaces

Author:
Jaehyun Hong

Journal:
Trans. Amer. Math. Soc. **359** (2007), 2361-2381

MSC (2000):
Primary 14C25, 32M15, 14M15

Published electronically:
June 13, 2006

MathSciNet review:
2276624

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Abstract: In this paper we study the space of effective -cycles in with the homology class equal to an integral multiple of the homology class of Schubert variety of type . When is a proper linear subspace of a linear space in , we know that is already complicated. We will show that for a smooth Schubert variety in a Hermitian symmetric space, any irreducible subvariety with the homology class , , is again a Schubert variety of type , unless is a non-maximal linear space. In particular, any local deformation of such a smooth Schubert variety in Hermitian symmetric space is obtained by the action of the Lie group .

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Additional Information

**Jaehyun Hong**

Affiliation:
Research Institute of Mathematics, Seoul National University, San 56-1 Sinrim-dong Kwanak-gu, Seoul, 151-747 Korea

Email:
jhhong@math.snu.ac.kr

DOI:
https://doi.org/10.1090/S0002-9947-06-04041-4

Keywords:
Analytic cycles,
Hermitian symmetric spaces,
Schubert varieties

Received by editor(s):
October 26, 2004

Received by editor(s) in revised form:
April 13, 2005

Published electronically:
June 13, 2006

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.