Rigidity of smooth Schubert varieties in Hermitian symmetric spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Rigidity of smooth Schubert varieties in Hermitian symmetric spaces

Authors:	Jaehyun Hong

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

Abstract:	In this paper we study the space $\mathcal{Z}_k(G/P, rX_w])$ 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 $\mathbb{P}^k$ of a linear space $\mathbb{P}^n$ in $G/P \subset \mathbb{P}(V)$ , we know that $\mathcal{Z}_k(\mathbb{P}^n, r\mathbb{P}^k])$ is already complicated. We will show that for a smooth Schubert variety in a Hermitian symmetric space, any irreducible subvariety with the homology class , $r\in \mathbb{Z}$ , 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 .

Keywords:	Analytic cycles Hermitian symmetric spaces Schubert varieties

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