Abstract
In this paper we present the first example of a primitive, totally geodesic subvariety $F \subset \mathcal{M}_{g,n}$ with $\mathrm{dim}(F)>1$. The variety we consider is a surface $F \subset \mathcal{M}_{1,3}$ defined using the projective geometry of plane cubic curves. We also obtain a new series of Teichmüller curves in $\mathcal{M}_4$, and new $\mathrm{SL}_2(\mathbb{R})$-invariant varieties in the moduli spaces of quadratic differentials and holomorphic 1-forms.
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[Wright:fields] A. Wright, "The field of definition of affine invariant submanifolds of the moduli space of abelian differentials," Geom. Topol., vol. 18, iss. 3, pp. 1323-1341, 2014.
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title = {The field of definition of affine invariant submanifolds of the moduli space of abelian differentials},
year = {2014},
pages = {1323--1341},
} -
[Wright:cylinders] A. Wright, "Cylinder deformations in orbit closures of translation surfaces," Geom. Topol., vol. 19, iss. 1, pp. 413-438, 2015.
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number = {1},
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mrreviewer = {Jayadev S. Athreya},
title = {Cylinder deformations in orbit closures of translation surfaces},
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pages = {413--438},
} -
[Zorich:survey] A. Zorich, "Flat surfaces," in Frontiers in Number Theory, Physics, and Geometry. I, New York: Springer-Verlag, 2006, pp. 437-583.
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Full Article