Teichmüller curves in the Deligne-Mumford compactification

Abstract

<p>We study the intersection of the closure of a Teichmüller curve and the compactification divisor in the Delinge-Mumford compactification of the moduli space of Riemann surfaces. As an application, we evaluate the first Mumford-Morita class on the homology class defined by an abelian Teichmüller curve. We deduce the Weil-Petersson area of a Teichmüller curve, which depends mainly on the curve's Euler characteristics.</p>