On the Family of Pentagonal curves of genus 6 and associated modular forms on the Ball

Details On the Family of Pentagonal curves of genus 6 and associated modular forms on the Ball On the Family of Pentagonal curves of genus 6 and associated modular forms on the Ball

2000-09-21

arxiv.org/abs/math/0009200v1

Mathematics

Algebraic Geometry

latex2e + amsart

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On the Family of Pentagonal curves of genus 6 and associated modular forms on the Ball does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Family of Pentagonal curves of genus 6 and associated modular forms on the Ball, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Family of Pentagonal curves of genus 6 and associated modular forms on the Ball will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-532506