Classification of higher rank orbit closures in

  • David Aulicino

    University of Chicago, USA
  • Duc-Manh Nguyen

    Université de Bordeaux I, Talence, France
  • Alex Wright

    Stanford University, USA

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 the only orbit closures are closed orbits, the Prym locus , and .

Together with work of Matheus–Wright, this implies that there are only finitely many non-arithmetic closed orbits (Teichmüller curves) in outside of the Prym locus.

Cite this article

David Aulicino, Duc-Manh Nguyen, Alex Wright, Classification of higher rank orbit closures in . J. Eur. Math. Soc. 18 (2016), no. 8, pp. 1855–1872

DOI 10.4171/JEMS/631