Periods of Strebel Differentials and Algebraic Curves Defined over the Field of Algebraic Numbers
Open Access Publications from the University of California

## Periods of Strebel Differentials and Algebraic Curves Defined over the Field of Algebraic Numbers

• Author(s): Mulase, Motohico
• Penkava, Michael
• et al.

## Published Web Location

https://arxiv.org/pdf/math/0107119.pdf
No data is associated with this publication.
Abstract

In \cite{MP} we have shown that if a compact Riemann surface admits a Strebel differential with rational periods, then the Riemann surface is the complex model of an algebraic curve defined over the field of algebraic numbers. We will show in this article that even if all geometric data are defined over $\overline{\mathbb{Q}}$, the Strebel differential can still have a transcendental period. We construct a Strebel differential $q$ on an arbitrary complete nonsingular algebraic curve $C$ defined over $\overline{\mathbb{Q}}$ such that (i) all poles of $q$ are $\overline{\mathbb{Q}}$-rational points of $C$; (ii) the residue of $\sqrt{q}$ at each pole is a positive integer; and (iii) $q$ has a transcendental period.

Item not freely available? Link broken?
Report a problem accessing this item