Splitting mixed Hodge structures over affine invariant manifolds

• 成果类型: Article
• 署名作者: Filip, Simion
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.183.2.5
• 发表日期: 2016
• 页码: 681-713
• 关键词: teichmuller-curves; moduli space; veech surfaces; FLOWS; transformations; differentials; components

摘要

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 Moller. 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.