A Topological Characterization of the Middle Perversity Intersection Complex for Arbitrary Complex Algebraic Varieties
Abstract
For an arbitrary complex algebraic variety which is not necessarily pure dimensional, the intersection complex can be defined as the direct sum of the Deligne-Goresky-MacPherson intersection complexes of each irreducible component. We give two axiomatic topological characterizations of the middle perversity direct sum intersection complex, one stratification dependent and the other stratification independent. To accomplish this, we show that this direct sum intersection complex can be constructed using Deligne's construction in the more general context of topologically stratified spaces. A consequence of these characterizations is the invariance of this direct sum intersection complex under homeomorphisms.
Cite
@article{arxiv.1905.12715,
title = {A Topological Characterization of the Middle Perversity Intersection Complex for Arbitrary Complex Algebraic Varieties},
author = {Ben Wu},
journal= {arXiv preprint arXiv:1905.12715},
year = {2020}
}
Comments
27 pages. Revised introduction and several remarks added. The article is now also available on the website of the Journal of Singularities http://www.journalofsing.org/volume20/article3.html