Rank two affine submanifolds in $\mathcal{H}(2,2)$ and $\mathcal{H}(3,1)$

Abstract

We classify all rank two affine manifolds in strata in genus three with two zeros. This confirms a conjecture of Maryam Mirzakhani in these cases. Several technical results are proven for all strata in genus three, with the hope that they may shed light on a complete classification of rank two manifolds in genus three.

arXiv comment63 pages, 28 figures

References in corpus (5)

• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Semisimplicity and rigidity of the Kontsevich-Zorich cocycle
• Splitting mixed Hodge structures over affine invariant manifolds
• Cylinder deformations in orbit closures of translation surfaces
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Cited by in corpus (3)

• Full rank affine invariant submanifolds
• GL(2,R) Orbit Closures in Hyperelliptic Components of Strata
• Orbifold points on Prym-Teichmüller curves in genus three