A criterion for being a Teichm\"uller curve
Elise Goujard
TL;DR
This paper introduces a new criterion, similar to M"oller's, for identifying Teichm"uller curves within the moduli space of Riemann surfaces, supported by a dynamical proof.
Contribution
It provides a novel criterion and a dynamical proof for recognizing Teichm"uller curves in the moduli space, extending previous methods.
Findings
New criterion for Teichm"uller curves detection
Dynamical proof of the criterion
Application to complex curves in moduli space
Abstract
Teichm\"uller curves play an important role in the study of dynamics in polygonal billiards. In this article, we provide a criterion similar to the original M\"oller'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 Teichm\"uller curve, and give a dynamical proof of this criterion.
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Taxonomy
TopicsMathematical Dynamics and Fractals · History and Theory of Mathematics · Analytic and geometric function theory