  The purpose of this article is to investigate the intersection cohomology for
algebraic varieties with torus action. Given an algebraic torus $\mathbb{T}$,
one of our result determines the intersection cohomology Betti numbers of any
normal projective $\mathbb{T}$-variety admitting an algebraic curve as global
quotient. The calculation is expressed in terms of a combinatorial description
involving a divisorial fan which is the analogous of the defining fan of a
toric variety. Our main tool to obtain this computation is a description of the
decomposition theorem in this context.
