## Journal of Differential Geometry

### Period integrals and the Riemann–Hilbert correspondence

#### Abstract

A tautological system, introduced in [20][21], arises as a regular holonomic system of partial differential equations that governs 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 [5], 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.

#### Article information

Source
J. Differential Geom., Volume 104, Number 2 (2016), 325-369.

Dates
First available in Project Euclid: 13 October 2016

https://projecteuclid.org/euclid.jdg/1476367060

Digital Object Identifier
doi:10.4310/jdg/1476367060

Mathematical Reviews number (MathSciNet)
MR3557307

Zentralblatt MATH identifier
06654475

#### Citation

Huang, An; Lian, Bong H.; Zhu, Xinwen. Period integrals and the Riemann–Hilbert correspondence. J. Differential Geom. 104 (2016), no. 2, 325--369. doi:10.4310/jdg/1476367060. https://projecteuclid.org/euclid.jdg/1476367060