Link Bundles and Intersection Spaces of Complex Toric Varieties
Markus Banagl and Shahryar Ghaed Sharaf
Journal of Singularities
volume 28 (2025), 55-103
Received: 26 June 2024.
Abstract:
There exist several homology theories for singular spaces that satisfy generalized Poincaré duality, including Goresky-MacPherson's intersection homology, Cheeger's L^2 cohomology and the homology of intersection spaces. The intersection homology and L^2 cohomology of toric varieties is known. Here, we compute the rational homology of intersection spaces of complex 3-dimensional toric varieties and compare it to intersection homology. To achieve this, we analyze cell structures and topological stratifications of these varieties and determine compatible structures on their singularity links. In particular, we compute the homology of links in 3-dimensional toric varieties. We find it convenient to use the concept of a rational homology stratification. It turns out that the intersection space homology of a toric variety, contrary to its intersection homology, is not combinatorially invariant and thus retains more refined information on the defining fan.
2020 Mathematical Subject Classification:
55N33, 14M25, 57S12, 57N80
Key words and phrases:
Toric Varieties, Intersection Homology, Stratified Spaces
Author(s) information:
Markus Banagl
Institut für Mathematik
Universität Heidelberg
Im Neuenheimer Feld 205
69120 Heidelberg, Germany
email: banagl@mathi.uni-heidelberg.de
Shahryar Ghaed Sharaf
Fakultät für Mathematik und Informatik
Friedrich-Schiller-Universität Jena
Ernst-Abbe-Platz 2
07743 Jena, Germany
email: shahryar.ghaed.sharaf@uni-jena.de