Rigidity of smooth Schubert varieties in Hermitian symmetric spaces

Details Rigidity of smooth Schubert varieties in Hermitian symmetric spaces Rigidity of smooth Schubert varieties in Hermitian symmetric spaces

2004-10-06

arxiv.org/abs/math/0410138v3

Mathematics

Differential Geometry

17 pages. To appear in Transactions of AMS

Scientific paper

Schubert varieties are irreducible subvarieties of homogeneous manifold, which are important to understand the geometry of homogeneous manifold G/P and the action of the semisimple Lie group G. Consider the space of effective cycles in G/P with homology class equal to an integral multiple of the homology class of a Schubert variety X_w of type w. We will show that for a smooth Schubert variety X_w in Hermitian symmetric space with trivial exceptions, this cycle space is simple: any irreducible subvariety X with homology class [X]=r[X_w] is again a Schubert variety of type w.

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