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. 1855–1872DOI 10.4171/JEMS/631