Talk 10909 data/Fall

Algebraic Geometry Seminar
Friday, October 4, 2019, 3:15pm, 119 Physics
Jaehyun Hong (Korea Institute for Advanced Study)
Rigidity of Schubert varieties in rational homogeneous manifolds of Picard number one

Given a rational homogeneous manifold S=G/P of Picard number one and a Schubert variety S_0 of S, the pair (S,S_0) is said to be homologically rigid if any subvariety of S having the same homology class as S_0 must be a translate of S_0 by G. The pair (S,S_0) is said to be Schur rigid if any subvariety of S with homology class equal to a multiple of the homology class of S_0 must be a sum of translates of S_0. In this talk we use the theory of minimal rational curves to get homological rigidity and apply a refined form of transversality to reduce Schur rigidity to homological rigidity, proving that (S,S_0) exhibits Schur rigidity whenever S_0 is a non-linear smooth Schubert variety. This is joint work with N. Mok.

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