Related papers: Real intersection homology
We show that for a complete complex algebraic variety the pure component of homology coincides with the image of intersection homology. Therefore pure homology is topologically invariant. To obtain slightly more general results we introduce…
A homology stratification is a filtered space with local homology groups constant on strata. Despite being used by Goresky and MacPherson [Intersection homology theory: II, Inventiones Mathematicae, 71 (1983) 77-129] in their proof of…
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…
The rational homology group of the order complex of non-even partitions of a finite set is calculated. A twisted version of the Goresky-MacPherson approach to similar homology calculations is proposed.
We indicate two short proofs of the Goresky-MacPherson topological invariance of intersection homology. One proof is very short but requires the Goresky-MacPherson support and cosupport axioms; the other is slightly longer but does not…
Numerical equivalence of algebraic cycles is defined abstractly by intersection numbers. Classically, for smooth complex proper toric varieties, the quotients by numerical equivalence with rational coefficients can be described…
As Goresky and MacPherson intersection homology is not the homology of a space, there is no preferred candidate for intersection homotopy groups. Here, they are defined as the homotopy groups of a simplicial set which P. Gajer associates to…
There exist several homology theories for singular spaces that satisfy generalized Poincar\'e duality, including Goresky-MacPherson's intersection homology, Cheeger's $L^2$ cohomology and the homology of intersection spaces. The…
We consider a possibility of the existence of intersection homology morphism, which would be associated to a map of analytic varieties. We assume that the map is an inclusion of codimension one. Then the existence of a morphism follows from…
We provide a novel proof of the homological excess intersection formula for local complete intersections. The novelty is that the proof makes use of global morphisms comparing the intersections to a self intersection.
We introduce techniques of Suslin, Voevodsky, and others into the study of singular varieties. Our approach is modeled after Goresky-MacPherson intersection homology. We provide a formulation of perversity cycle spaces leading to perversity…
The aim of this paper is to study the behavior of Hodge-theoretic (intersection homology) genera and their associated characteristic classes under proper morphisms of complex algebraic varieties. We obtain formulae that relate (parametrized…
We show that the intersection pairing on our real intersection homology groups is not a dual pairing in general.
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
We obtain criteria for detecting complete intersections in projective varieties. Motivated by a conjecture of Hartshorne concerning subvarieties of projective spaces, we investigate situations when two-codimensional smooth subvarieties of…
We compare the sheaf-theoretic and singular chain versions of Poincare duality for intersection homology, showing that they are isomorphic via naturally defined maps. Similarly, we demonstrate the existence of canonical isomorphisms between…
We extend the notions of complete intersection dimension and lower complete intersection dimension to the category of complexes with finite homology and verify basic properties analogous to those holding for modules. We also discuss the…
Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration…
Let $f:X-->Y$ be a map of algebraic varieties. Barthel, Brasselet, Fieseler, Gabber and Kaup have shown that there exists a homomorphism of intersection homology groups $f^*:IH^*(Y)-->IH^*(X)$ compatible with the induced homomorphism on…
We define a variant of intersection space theory that applies to many compact complex and real analytic spaces $X$, including all complex projective varieties; this is a significant extension to a theory which has so far only been shown to…