  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.
