Mathematical Research Letters

Volume 19 (2012)

Number 4

A criterion for being a Teichmüller curve

Pages: 847 – 854



Elise Goujard (IRMAR, Université de Rennes 1, Campus de Beaulieu, Rennes, France)


Teichmüller curves play an important role in the study of dynamics in polygonal billiards. In this article, we provide a criterion similar to the original Möller’s criterion, to detect whether a complex curve, embedded in the moduli space of Riemann surfaces and endowed with a line subbundle of the Hodge bundle, is a Teichmüller curve, and give a dynamical proof of this criterion.

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