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홈 > 학술정보 >학술행사 > 세미나
한국고등과학원 세미나

Title
Standard embeddings of smooth Schubert varieties in symplectic Grassmannians
Speaker
Park, Kyeong-Dong   (IBS-CGP )
Date
2017-01-10 11:00:00
Host
KIAS
Place
1424
Abstract
A smooth Schubert variety of a rational homogeneous manifold G/P is canonically embedded in G/P by an equivariant embedding induced from the inclusion of a Borel subgroup. By a standard embedding of the smooth Schubert variety into G/P, we will mean the composite of the canonical equivaiant embedding and an element of the automorphism group of G/P. We characterize standard embeddings of smooth Schubert varieties in symplectic Grassmannians by means of varieties of minimal rational tangents.Smooth Schubert varieties have been classified by using combinatorial and geometric methods. When G/P is associated to a long simple root, any smooth Schubert variety in G/P is a homogeneous submanifold associated to a subdiagram of the marked Dynkin diagram of G/P. On the other hand, when G/P is associated to a short simple root, there is a smooth Schubert variety which is not homogeneous. From the classification of smooth Schubert varieties in the symplectic Grassmannians and the previous results on standard embeddings, it suffices to consider odd symplectic Grassmannians for smooth Schubert varieties in the symplectic Grassmannians. This is ongoing work with Shin-Young Kim.
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