The interplay between the characteristic and resonance varieties of a group leads to new and powerful obstructions to formality and quasi-projectivity. When combined with a complex analogue of the Bestvina-Brady Morse theory for groups, this yields an answer to a question of Koll'ar on the existence (up to commensurability) of quasi-projective classifying spaces for the fundamental groups of smooth projective varieties. This is joint work with Alex Dimca and Stefan Papadima. |