Splitting mixed Hodge structures over affine invariant manifolds

Abstract

We prove that affine invariant manifolds in strata of flat surfaces are algebraic varieties. The result is deduced from a generalization of a theorem of Möller. Namely, we prove that the image of a certain twisted Abel-Jacobi map lands in the torsion of a factor of the Jacobians. This statement can be viewed as a splitting of certain mixed Hodge structures.

Updated according to referee remarks

Cited by in corpus (20)

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• Zero Lyapunov exponents and monodromy of the Kontsevich-Zorich cocycle
• Full rank affine invariant submanifolds
• Marked points on translation surfaces
• Real multiplication through explicit correspondences
• GL(2,R)-Invariant Measures in Marked Strata: Generic Marked Points, Earle-Kra for Strata, and Illumination
• GL(2,R) Orbit Closures in Hyperelliptic Components of Strata
• Affine geometry of strata of differentials
• Eigenvalues of Curvature, Lyapunov exponents and Harder-Narasimhan filtrations
• Rank two affine submanifolds in $\mathcal{H}(2,2)$ and $\mathcal{H}(3,1)$
• Equations of linear subvarieties of strata of differentials
• The WYSIWYG compactification
• Measure bound for translation surfaces with short saddle connections
• Hodge and Teichmüller
• Teichmüller curves in genus two: Square-tiled surfaces and modular curves
• Coarse density of subsets of $M_g$
• Hyperelliptic Gorenstein curves and logarithmic differentials
• Continuity of the orthogeodesic foliation and ergodic theory of the earthquake flow
• Bi-algebraic geometry of strata of differentials in genus zero
• Teichmüller curves in hyperelliptic components of meromorphic strata