A discreteness criterion for subgroups of PU(2,1) with screw parabolic elements

We establish a discreteness criterion for Γ⊂PU(2,1) with a screw parabolic element g, which can be viewed as a generalization of Shimizu's lemma. Our method relies upon the geometry of Margulis region. It allows us to get rid of the restriction on rotation angle 2πα of g in [4,7]. Besides, an explicit region precisely invariant under the stabilizer of the fixed point of g in Γ is given.