Cubic curves and totally geodesic subvarieties of moduli space

In this paper we present the first example of a primitive, totally geodesic subvariety F⊂g,nF⊂Mg,n with dim(F)>1dim(F)>1. The variety we consider is a surface F⊂1,3F⊂M1,3 defined using the projective geometry of plane cubic curves. We also obtain a new series of Teichmüller curves in 4M4, and new SL2(ℝ)SL2(R)-invariant varieties in the moduli spaces of quadratic differentials and holomorphic 1-forms.Mathematic