  We study intersection cohomology of character varieties for punctured Riemann
surfaces with prescribed monodromies around the punctures. Relying on previous
result from Mellit for semisimple monodromies we compute the intersection
cohomology of character varieties with monodromies of any Jordan type. This
proves the Poincar\'e polynomial specialization of a conjecture from Letellier.

Algebraic Geometry