Base manifolds for fibrations of projective irreducible symplectic manifolds
Base manifolds for fibrations of projective irreducible symplectic manifolds
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DOI：
10.1007/s00222-008-0143-9
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发表时间：
2007-11
影响因子：
3.1
通讯作者：
Jun-Muk Hwang
中科院分区：
文献类型：
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作者：
Jun-Muk Hwang
给定一个2n维的射影不可约辛流形M，一个射影流形X和一个具有正维连通纤维的满射全纯映射：M→ X，我们证明了X是n维射影空间的双全纯映射。证明是通过利用两个几何结构在一般点的X：所产生的仿射结构的拉格朗日fibration的作用变量和结构定义的各种最小合理的切线Fano manifoldX。
Given a projective irreducible symplectic manifoldMof dimension 2n, a projective manifoldXand a surjective holomorphic mapf:M→Xwith connected fibers of positive dimension, we prove thatXis biholomorphic to the projective space of dimensionn. The proof is obtained by exploiting two geometric structures at general points ofX: the affine structure arising from the action variables of the Lagrangian fibrationfand the structure defined by the variety of minimal rational tangents on the Fano manifoldX.