JournalsjemsVol. 18, No. 8pp. 1855–1872

Classification of higher rank orbit closures in Hodd(4){\mathcal H^{\mathrm{odd}}(4)}

  • David Aulicino

    University of Chicago, USA
  • Duc-Manh Nguyen

    Université de Bordeaux I, Talence, France
  • Alex Wright

    Stanford University, USA
Classification of higher rank orbit closures in ${\mathcal H^{\mathrm{odd}}(4)}$ cover
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Abstract

The moduli space of genus 3 translation surfaces with a single zero has two connected components. We show that in the odd connected component Hodd(4){\mathcal H^{\mathrm{odd}}(4)} the only GL+(2,R){GL^+(2,\mathbb R)} orbit closures are closed orbits, the Prym locus Q~(3,13){\tilde{\mathcal{Q}}(3,-1^3)}, and Hodd(4){\mathcal H^{\mathrm{odd}}(4)}.

Together with work of Matheus–Wright, this implies that there are only finitely many non-arithmetic closed orbits (Teichmüller curves) in Hodd(4)\mathcal H^{\mathrm{odd}}(4) outside of the Prym locus.

Cite this article

David Aulicino, Duc-Manh Nguyen, Alex Wright, Classification of higher rank orbit closures in Hodd(4){\mathcal H^{\mathrm{odd}}(4)}. J. Eur. Math. Soc. 18 (2016), no. 8, pp. 1855–1872

DOI 10.4171/JEMS/631