Classification of higher rank orbit closures in H^{odd}(4)

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 H^{odd}(4) the only GL^+(2,R) orbit closures are closed orbits, the Prym locus Q(3,-1^3), and H^{odd}(4). Together with work of Matheus-Wright, this implies that there are only finitely many non-arithmetic closed orbits (Teichmuller curves) in H^{odd}(4) outside of the Prym locus.

23 pages; minor revision

References in corpus (2)

• Semisimplicity and rigidity of the Kontsevich-Zorich cocycle
• Non-Veech surfaces in H^hyp(4) are generic

Cited by in corpus (2)

• The Deligne-Mumford and the Incidence Variety Compactifications of the Strata of $\Omega {\mathcal{M}}_g$
• Non-Veech surfaces in H^hyp(4) are generic