Classification of higher rank orbit closures in Hodd(4)

الأصل · EN

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 GL+(2,R) orbit closures are closed orbits, the Prym locus Q(3,-1³), and Hodd(4). Together with work of Matheus-Wright, this implies that there are only finitely many non-arithmetic closed orbits (Teichmuller curves) in Hodd(4) outside of the Prym locus.