On intersection cohomology with torus action of complexity one, II

Abstract: We show that the components, appearing in the decomposition theorem for contraction maps of torus actions of complexity one, are intersection cohomology complexes of even codimensional subvarieties. As a consequence, we obtain the vanishing of the odd dimensional intersection cohomology for rational complete varieties with torus action of complexity one. The article also presents structural results on linear torus action in order to compute the intersection cohomology from the weight matrix. In particular, we determine the intersection cohomology Betti numbers of affine trinomial hypersurfaces in terms of their defining equation.