On intersection cohomology with torus action of complexity one, II
Algebraic Geometry
2026-03-10 v2 Algebraic Topology
Combinatorics
Complex Variables
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.
Keywords
Cite
@article{arxiv.2109.12641,
title = {On intersection cohomology with torus action of complexity one, II},
author = {Marta Agustin Vicente and Narasimha Chary Bonala and Kevin Langlois},
journal= {arXiv preprint arXiv:2109.12641},
year = {2026}
}
Comments
Final version. To appear in Transformation Groups