Nilpotent groups and universal coverings of smooth projective varieties (Q1364626)

In this paper we prove that the universal covering of a smooth projective variety \(X\) is holomorphically convex if \(\pi_1(X)\) is nilpotent. This is a partial case of the Shafarevich conjecture saying that the universal coverings of smooth projective varieties are holomorphically convex. The technique used in the proof is the strictness property of the mixed Hodge structures. At the end we also exhibit some properties of the solvable linear fundamental groups of smooth projective varieties.