Period Integrals and the Riemann-Hilbert Correspondence

An Huang Harvard University Bong H. Lian Brandeis University Xinwen Zhu California Institute of Technology


Silver Award Paper in 2017

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.
Period Integrals, Riemann-Hilbert Correspondence
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  title={Period Integrals and the Riemann-Hilbert Correspondence},
  author={An Huang, Bong H. Lian, and Xinwen Zhu},
An Huang, Bong H. Lian, and Xinwen Zhu. Period Integrals and the Riemann-Hilbert Correspondence. 2014.
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