Bicanonical and adjoint linear systems on surfaces of general type.

This note contains a new proof of a theorem of Gang Xiao saying that the bicanonical map of a surface S of general type is generically ?nite if and only if p2(S) > 2. Such properties are also studied for adjoint linear systems |KS + L|, where L is any divisor with h0(S,OS(L)) = 2.