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In this paper, we study the rigidity under K\"{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.
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참고문헌 (21)
참고문헌 신청
D. N. Akhiezer / 1995 / Lie Group Actions in Complex Analysis / Vieweg+Teubner Verlag
B. Fu / 2012 / Classification of non-degenerate projective varieties with nonzero prolongation and application to target rigidity / Invent. Math 189(2):457~513
J.-M. Hwang / 2001 / Geometry of minimal rational curves on Fano manifolds, School on Vanishing Theorems and Effective Results in Algebraic Geometry (Trieste, 2000) :335~393
J.-M. Hwang / 2010 / Deformation of the space of lines on the 5-dimensional hyperquadric
J.-M. Hwang / 1998 / Rigidity of irreducible Hermitian symmetric spaces of the compact type under K¨ahler deformation / Invent. Math 131(2):393~418
B. Fu / 2012 / Classification of non-degenerate projective varieties with nonzero prolongation and application to target rigidity / Invent. Math 189(2):457~513
J.-M. Hwang / 2001 / Geometry of minimal rational curves on Fano manifolds, School on Vanishing Theorems and Effective Results in Algebraic Geometry (Trieste, 2000) :335~393
J.-M. Hwang / 2010 / Deformation of the space of lines on the 5-dimensional hyperquadric
J.-M. Hwang / 1998 / Rigidity of irreducible Hermitian symmetric spaces of the compact type under K¨ahler deformation / Invent. Math 131(2):393~418
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