Projective representations of fundamental groups of quasiprojective   varieties: a realization and a lifting result
  We discuss two results about projective representations of fundamental groups of quasiprojective varieties. The first is a realization result which, under a nonresonance assumption, allows to realize such representations as monodromy representations of flat projective logarithmic connections. The second is a lifting result: any representation as above, after restriction to a Zariski open set and finite pull-back, can be lifted to a linear representation. 
Ga\"el Cousin
math.AG math.CV