Griffiths, PhillipPhillipGriffithsGreen, MarkMarkGreenKatzarkov, LudmilLudmilKatzarkov2022-10-192022-10-19https://hdl.handle.net/20.500.12111/8041I. Introduction and statements of results II. The nilpotent case III. The variation of Hodge structure and mixed Hodge structure cases IV. Further directionsWe shall show that a smooth, quasi-projective variety X has a holomorphically convex universal covering eX when (i) 1(X) is residually nilpotent and (ii) there is an admissable variation of mixed Hodge structure over X whose monodromy representation has a nite kernel, and where in each case a corresponding period mapping is assumed to be proper.en-USperiod mappingShafarevich mappingmixed Hodge structureJournal article