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This paper is devoted to the classification of connected components of Prym eigenform loci in the strata $$\mathcal H(2,2)^\mathrm{odd}$$ H(2,2)odd and $$\mathcal H(1,1,2)$$ H(1,1,2) of the bundle of Abelian differentials $$\Omega {\mathcal {M}}_3$$ ΩM3 over $${\mathcal {M}}_3$$ M3 . These loci, discovered by McMullen (Duke Math J 133:569–590, 2006), are $$\mathrm{GL}^+(2,\mathbb {R})$$ GL+(2,R)...
This paper follows on from Nguyen (Geom Funct Anal 20(1):192–228, 2010), in which we study flat surfaces with erasing forest, these surfaces are obtained by deforming the metric structure of translation surfaces, and their moduli space can be viewed as a deformation of the moduli space of translation surfaces. We showed that the moduli spaces of such surfaces are complex orbifolds, and admit a natural...
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