Zuo, Kang Kodaira dimension and Chern hyperbolicity of the Shafarevich maps for representations of \(\pi_ 1\) of compact Kähler manifolds. (English) Zbl 0838.14017 J. Reine Angew. Math. 472, 139-156 (1996). We prove that the Shafarevich variety is of general type and Chern hyperbolic for any Zariski dense representation of \(\pi_1\) of a compact Kähler manifold into an almost simple algebraic group. As a consequence we show that any reductive representation of \(\pi_1\) of a compact Kähler manifold of algebraic dimension or Kodaira dimension equal to zero always splits into a direct sum of one-dimensional representations after passing to a finite étale covering. Reviewer: K.Zuo (Kaiserslautern) Cited in 1 ReviewCited in 11 Documents MSC: 14F35 Homotopy theory and fundamental groups in algebraic geometry 14J45 Fano varieties 53C55 Global differential geometry of Hermitian and Kählerian manifolds Keywords:representation of fundamental group; Kähler manifolds; Shafarevich variety; Kodaira dimension PDFBibTeX XMLCite \textit{K. Zuo}, J. Reine Angew. Math. 472, 139--156 (1996; Zbl 0838.14017) Full Text: DOI Crelle EuDML