On singular fibres of Lagrangian fibrations over holomorphic symplectic manifolds
On singular fibres of Lagrangian fibrations over holomorphic symplectic manifolds
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关于全纯辛流形上拉格朗日纤维的奇异纤维
DOI：
10.1007/s002080100251
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发表时间：
2001
影响因子：
1.4
通讯作者：
D. Matsushita
中科院分区：
文献类型：
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作者：
D. Matsushita
我们对四维全纯辛流形上投影拉格朗日纤维的判别轨迹的一般点上的奇异纤维进行了分类。奇异纤维fi是以下任意一种：fi是椭圆曲线与Kodaira奇异纤维的乘积同构，直至有限未分枝覆盖；fi是由最小椭圆直纹曲面的几个副本组成的正交品种，其对偶图为类型或的Dynkin图。此外，我们还展示了上述所有类型的单一纤维实际上都存在。
We classify singular fibres over general points of the discriminant locus of projective Lagrangian fibrations over 4-dimensional holomorphic symplectic manifolds. The singular fibreFis the following either one:Fis isomorphic to the product of an elliptic curve and a Kodaira singular fibre up to finite unramified covering orFis a normal crossing variety consisting of several copies of a minimal elliptic ruled surface of which the dual graph is Dynkin diagram of typeor. Moreover, we show all types of the above singular fibres actually occur.