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

2013/08/27 by Aulicino, David, Nguyen, Duc-Manh, Wright, Alex
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1308.5879

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,-1³), 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.

Related

• Non-Veech surfaces in H^hyp(4) are generic
• Finiteness of Teichmüller curves in non-arithmetic rank 1 orbit closures
• High rank invariant subvarieties
• Rank One Orbit Closures in H^hyp(g-1,g-1)
• Completely periodic directions and orbit closures of many pseudo-Anosov Teichmueller discs in Q(1,1,1,1)