Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Family of Pentagonal curves of genus 6 and associated modular
  forms on the Ball   In this article we study the inverse of the period map for the family
$\mathcal{F}$ of complex algebraic curves of genus 6 equipped with an
automorphism of order 5. This is a family with 2 parameters, and is fibred over
a certain type of Del Pezzo surace. The period satisfies the hypergeometric
differential equation for Appell's $F_1({3/5},{3/5},{2/5},{6/5})$ of two
variables after a certain normalization of the variable parameter. This
differential equation and the family $\mathcal{F}$ are studied by G. Shimura
(1964), T. Terada (1983, 1985), P. Deligne - G.D. Mostow (1986) and T.
Yamazaki- M. Yoshida(1984). Recently M. Yoshida presented a new approch using
the concept of configration space. Based on their results we show the
representation of the inverse of the period map in terms of Riemann theta
constants. This is the first variant of the work of H. Shiga (1981) and K.
Matsumoto (1989, 2000) to the co-compact case.

22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int