2012/09/13 by Artur Avila, Avila, Artur, Alex Eskin +4 · 29 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Bundle #Cohomology #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds #Hodge theory #Invariant (physics) #Mathematical physics #Mathematics #Moduli space #Normal bundle #Pure mathematics #Symplectic geometry #Tangent bundle #Tangent space #Vector bundle #math.AG #math.DS #math.GT
paper · pdf · doi:10.48550/arxiv.1209.2854
published in arXiv (Cornell University) (Cornell University) · 23 pages. To appear in Crelle's journal
openalex publication_date 2012/09/13 · arxiv created 2014/12/04 · arxiv updated 2014/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose N is an affine SL(2,R)-invariant submanfold of the moduli space of pairs (M,w) where M is a curve, and w is a holomorphic 1-form on M. We show that the Forni bundle of N (i.e. the maximal SL(2,R)-invariant isometric subbundle of the Hodge bundle of N) is always flat and is always orthogonal to the tangent space of N. As a corollary, it follows that the Hodge bundle of N is semisimple.