Classification of higher rank orbit closures in Hodd(4).

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) the only G+(2,ℝ) orbit closures are closed orbits, the Prym locus ..., and Hodd(4) Together with work of Matheus--Wright, this implies that there are only finitely many nonarithmetic closed orbits (Teichmüller curves) in Hodd(4) outside of the Prym locus. [ABSTRACT FROM AUTHOR]