Slope and Siegel-Veech constant of Teichmüller curves                               
-- Dawei Chen, September 17, 2010                
                                 
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We study the algebro-geometric aspect of Teichm&uuml;ller curves
parameterizing square-tiled Riemann surfaces (i.e. covers of
elliptic curves with a unique branch point). The results can be
applied to produce rigid curves on the moduli space of pointed
rational curves, calculate the Siegel-Veech constants on the
moduli space of Abelian differentials, and bound the cone of
effective divisors on the moduli space of curves.