The image in Mg of strata of meromorphic and quadratic differentials

Abstract

We compute the dimension of the image of the map πZ:Z→Mg forgetting the markings, where Z is a connected component of the stratum Hkg(μ) of k-differentials with an assigned partition μ, for the cases when k=1 with meromorphic partition and k=2 when the quadratic differentials have at worst simple poles.