Journal of Differential Geometry

Period integrals and the Riemann–Hilbert correspondence

An Huang, Bong H. Lian, and Xinwen Zhu

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 13 October 2016

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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.

Export citation