Period Integrals and the Riemann-Hilbert Correspondence
Period Integrals and the Riemann-Hilbert Correspondence
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DOI：
10.4310/jdg/1476367060
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发表时间：
2013-03
期刊：
影响因子：
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通讯作者：
An Huang;B. Lian;Xinwen Zhu
中科院分区：
文献类型：
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作者：
An Huang;B. Lian;Xinwen Zhu
[16][17] 中引入的同义反复系统是作为偏微分方程的正则完整系统出现的，它控制复流形 $X$ 中完全交集族的周期积分，并配备了合适的李群作用。在[4]中推测了这种系统的完整秩的几何公式，并在假设下的射影齐次空间的情况下得到了验证。在本文中，我们完全普遍地证明了这个猜想。通过黎曼-希尔伯特对应和傅里叶变换，我们还将秩公式推广到具有群作用的任意射影流形。
A tautological system, introduced in [16][17], arises as a regular holonomic system of partial differential equations that govern the period integrals of a family of complete intersections in a complex manifold $X$, equipped with a suitable Lie group action. A geometric formula for the holonomic rank of such a system was conjectured in [4], and was verified for the case of projective homogeneous space under an assumption. In this paper, we prove this conjecture in full generality. By means of the Riemann-Hilbert correspondence and Fourier transforms, we also generalize the rank formula to an arbitrary projective manifold with a group action.