Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Period Integrals and the Riemann-Hilbert Correspondence   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.

11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn