An HuangHarvard UniversityBong H. LianBrandeis UniversityXinwen ZhuCalifornia Institute of Technology
mathscidoc:1608.01018
Silver Award Paper in 2017
2014
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.
@inproceedings{an2014period,
title={Period Integrals and the Riemann-Hilbert Correspondence},
author={An Huang, Bong H. Lian, and Xinwen Zhu},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160828143123061990476},
year={2014},
}
An Huang, Bong H. Lian, and Xinwen Zhu. Period Integrals and the Riemann-Hilbert Correspondence. 2014. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160828143123061990476.