Splitting mixed Hodge structures over affine invariant manifolds

2013/11/30 by Simion Filip · 1 citation
Mathematics · #math.DS #math.AG #math.GT

paper · pdf · doi:10.4007/annals.2016.183.2.5

published as Ann. of Math. (2) 183 (2016), no. 2, 681-713 · Updated according to referee remarks

arxiv created 2015/07/11 · arxiv updated 2017/10/31

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.

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