Geodesic
Cubic curves and totally geodesic subvarieties of moduli space
Curtis T. McMullen1 ; Ronen E. Mukamel2 ; Alex Wright3
1 Harvard University, Cambridge, MA
2 Rice University, Houston, TX
3 Stanford University, Stanford, CA
Annals of mathematics, Tome 185 (2017) no. 3, pp. 957-990.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2017.185.3.6

Curtis T. McMullen 1 ; Ronen E. Mukamel 2 ; Alex Wright 3

1 Harvard University, Cambridge, MA
2 Rice University, Houston, TX
3 Stanford University, Stanford, CA 
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Curtis T. McMullen; Ronen E. Mukamel; Alex Wright. Cubic curves and totally geodesic subvarieties of moduli space. Annals of mathematics, Tome 185 (2017) no. 3, pp. 957-990. doi : 10.4007/annals.2017.185.3.6. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.3.6/

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