Lagrangian Fibrations in Duality on Moduli Spaces of Rank 2 Logarithmic Connections Over the Projective Line
Lagrangian Fibrations in Duality on Moduli Spaces of Rank 2 Logarithmic Connections Over the Projective Line
复制标题
射影线上二阶对数连接模空间上的对偶拉格朗日纤维
DOI：
10.1093/imrn/rnt232
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发表时间：
2013
影响因子：
1
通讯作者：
Masa-Hiko Saito
中科院分区：
文献类型：
--
作者：
Frank Loray;Masa-Hiko Saito
本文研究了秩为2的n-n点对数联络的模空间。有两个自然的拉格朗日映射：一个指向相关的Fuchsian标量方程的表观奇点，另一个指向抛物丛的模。我们表明，这些是横向和对偶的对方。在n=5的情况下，我们恢复了美丽的几何的Del Pezzo曲面的次数为4。
We study the moduli space of logarithmic connections of rank 2 onminus n points with fixed spectral data. There are two natural Lagrangian maps: one toward apparent singularities of the associated Fuchsian scalar equation and another one toward moduli of parabolic bundles. We show that these are transversal and dual to each other. In case n=5, we recover the beautiful geometry of Del Pezzo surfaces of degree 4.