2020/04/08 by Indranil BIswas, BIswas, Indranil
Mathematics · #14D21 #32L10 #53C55 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.CV #math.DG #msc:14D21 #msc:32L10 #msc:53C55
paper · pdf · doi:10.48550/arxiv.2004.04089
Final version
arxiv created 2020/04/08 · arxiv updated 2020/04/09
A vector bundle E over a projective variety M is called finite if it satisfies a nontrivial polynomial equation with nonnegative integral coefficients. Introducing finite bundles, Nori proved that E is finite if and only if the pullback of E to some finite étale covering of M is trivializable \citeNo1. The definition of finite bundles extends naturally to holomorphic vector bundles over compact complex manifolds. We prove that a holomorphic vector bundle over a compact complex manifold M is finite if and only if the pullback of E to some finite étale covering of M is holomorphically trivializable. Therefore, E is finite if and only if it admits a flat holomorphic connection with finite monodromy.