Publication: Cubic curves and totally geodesic subvarieties of moduli space
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Date
2017
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Annals of Mathematics, Princeton U
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McMullen, Curtis, Ronen Mukamel, and Alex Wright. 2017. “Cubic Curves and Totally Geodesic Subvarieties of Moduli Space.” Annals of Mathematics 185 (3) (May 1): 957–990. doi:10.4007/annals.2017.185.3.6.
Abstract
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.
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Hodge theory, Teichmüller theory, dynamics on moduli spaces, elliptic curves
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