• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권1호
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• pp.13-23
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• 2015

We introduce a decomposition on a symplectic subspace determined by symplectic structure and study its properties. As a consequence, we give an elementary proof of the deformation of the Grassmannians of symplectic subspaces to the complex Grassmannians.

• 충청수학회지
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• 제36권1호
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• pp.1-8
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• 2023

Let C be a smooth projective curve and W a symplectic bundle over C of degree w. Let π : 𝕃𝔾(W) → C be the relative Lagrangian Grassmannian over C and S_d(W) be the space of Lagrangian subbundles of degree w -d. Then Kontsevich's space ${\bar{\mathcal{M}}}_g$(𝕃𝔾(W), β_d) of stable maps to 𝕃𝔾(W) is a compactification of S_d(W). In this article, we give an upper bound on the dimension of ${\bar{\mathcal{M}}}_g$(𝕃𝔾(W), β_d), which is an analogue of a result in [8] for the relative Lagrangian Grassmannian.

• 대한수학회지
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• 제53권3호
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• pp.489-501
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• 2016

In this paper, we study the rigidity under $K{\ddot{a}}hler$ deformation of the complex structure of odd Lagrangian Grassmannians, i.e., the Lagrangian case $Gr_{\omega}$(n, 2n+1) of odd symplectic Grassmannians. To obtain the global deformation rigidity of the odd Lagrangian Grassmannian, we use results about the automorphism group of this manifold, the Lie algebra of infinitesimal automorphisms of the affine cone of the variety of minimal rational tangents and its prolongations.