On the holomorphic convexity of the linear reductive spaces of a complex projective algebraic manifold

• 成果类型: Article
• 署名作者: Eyssidieux, P
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-003-0345-0
• 发表日期: 2004
• 页码: 503-564
• 关键词: harmonic maps; universal coverings; shafarevich maps; levi problem; REPRESENTATIONS; factorizations; HYPERBOLICITY; VARIETIES; currents; MODULI

摘要

Let X be a smooth connected compact projective variety over C. We study the Shafarevich conjecture concerning holomorphic convexity along the lines of Kollaar's approach, when the fundamental group of X admits large finite dimensionnal representations. We prove that, given nis an element ofN, the topological covering space (X) over tilde (n) of a projective algebraic compact complex manifold X corresponding to the intersection of the kernels of all linear reductive representations of pi(1)(X) to GL(n)(C) is holomorphically convex. In the surface case, this is a corollary of a theorem due to Katzarkov and Ramachandran.