PERIOD INTEGRALS AND THE RIEMANN-HILBERT CORRESPONDENCE

被引：0

作者：

Huang, An ^{[1
]}

Lian, Bong H. ^{[2
]}

Zhu, Xinwen ^{[3
]}

机构：

[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

[2] Brandeis Univ, Dept Math, Waltham, MA 02454 USA

[3] CALTECH, Dept Math, Pasadena, CA 91125 USA

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2016年 / 104卷 / 02期

基金：

美国国家科学基金会;

关键词：

HYPERGEOMETRIC-FUNCTIONS; SYSTEMS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：325 / 369

页数：45

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