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May 2017 Cubic curves and totally geodesic subvarieties of moduli space
Curtis McMullen, Ronen Mukamel, Alex Wright
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Ann. of Math. (2) 185(3): 957-990 (May 2017). DOI: 10.4007/annals.2017.185.3.6

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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Curtis McMullen. Ronen Mukamel. Alex Wright. "Cubic curves and totally geodesic subvarieties of moduli space." Ann. of Math. (2) 185 (3) 957 - 990, May 2017. https://doi.org/10.4007/annals.2017.185.3.6

Information

Published: May 2017
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2017.185.3.6

Rights: Copyright © 2017 Department of Mathematics, Princeton University

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Vol.185 • No. 3 • May 2017
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