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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title = {Schwarz triangle mappings and {T}eichmüller curves: the {V}eech-{W}ard-{B}ouw-{M}öller curves},
year = {2013},
pages = {776--809},
} -
[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.
@ARTICLE{Wright:fields, mrkey = {3254934},
number = {3},
issn = {1465-3060},
author = {Wright, Alex},
mrclass = {32G15 (30F60 37D40)},
doi = {10.2140/gt.2014.18.1323},
journal = {Geom. Topol.},
zblnumber = {1320.32019},
volume = {18},
mrnumber = {3254934},
fjournal = {Geometry \& Topology},
mrreviewer = {Jayadev S. Athreya},
title = {The field of definition of affine invariant submanifolds of the moduli space of abelian differentials},
year = {2014},
pages = {1323--1341},
} -
[Wright:cylinders]
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@ARTICLE{Wright:cylinders, mrkey = {3318755},
number = {1},
issn = {1465-3060},
author = {Wright, Alex},
mrclass = {32G15 (37D40)},
doi = {10.2140/gt.2015.19.413},
journal = {Geom. Topol.},
zblnumber = {1318.32021},
volume = {19},
mrnumber = {3318755},
fjournal = {Geometry \& Topology},
mrreviewer = {Jayadev S. Athreya},
title = {Cylinder deformations in orbit closures of translation surfaces},
year = {2015},
pages = {413--438},
} -
[Zorich:survey]
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@INCOLLECTION{Zorich:survey, mrkey = {2261104},
author = {Zorich, Anton},
mrclass = {37D40 (30F30 32G15 37D50 57M50)},
address = {New York},
publisher = {Springer-Verlag},
doi = {10.1007/978-3-540-31347-2_13},
zblnumber = {1129.32012},
mrnumber = {2261104},
booktitle = {Frontiers in Number Theory, Physics, and Geometry. {I}},
mrreviewer = {Thomas A. Schmidt},
title = {Flat surfaces},
pages = {437--583},
year = {2006},
}