Period Integrals and the Riemann-Hilbert Correspondence

  title={Period Integrals and the Riemann-Hilbert Correspondence},
  author={An Huang and Bong H. Lian and Xinwen Zhu},
  journal={arXiv: Algebraic Geometry},
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… 
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