A criterion for being a Teichmüller curve

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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Published 27 December 2012