Intersection homology Betti numbers
نویسنده
چکیده
A generalization of the formula of Fine and Rao for the ranks of the intersection homology groups of a complex algebraic variety is given. The proof uses geometric properties of intersection homology and mixed Hodge theory. The middle-perversity intersection homology with integral coefficients of a compact complex n-dimensional algebraic variety X with isolated singularities is well known to be [GM80]
منابع مشابه
Implementation of Stanley's algorithm for projective group imbeddings
Computing intersection cohomology Betti numbers is complicated by the fact that the usual long exact localization sequences in Borel–Moore homology do not carry over to the setting of intersection homology. Nevertheless, about 20 years ago, Richard Stanley had formulated a remarkable algorithm for computing the intersection cohomology Betti numbers of toric varieties. During the last few years,...
متن کاملLocal-global intersection homology
This paper defines new intersection homology groups. The basic idea is this. Ordinary homology is locally trivial. Intersection homology is not. It may have significant local cycles. A localglobal cycle is defined to be a family of such local cycles that is, at the same time, a global cycle. The motivating problem is the numerical characterisation of the flag vectors of convex polytopes. Centra...
متن کاملA New Index for Polytopes
A new index for convex polytopes is introduced. It is a vector whose length is the dimension of the linear span of the flag vectors of polytopes. The existence of this index is equivalent to the generalized Dehn-Sommerville equations. It can be computed via a shelling of the polytope. The ranks of the middle perversity intersection homology of the associated toric variety are computed from the ...
متن کاملTest Functions, Partitioning and Concentration Phenomena in Toric Geometry
We discuss simple partitioning phenomena for intersection rings of certain toric varieties, and apply this to prove the following results. ̋ We generalize a result of Gräbe, proving that Stanley–Reisner rings of homology spheres are Gorenstein. ̋ We give a new and direct proof of a theorem of the authors due to which the cohomology rings of matroids are Poincare duality algebras. ̋ We prove a conj...
متن کاملBounds on Genus and Geometric Intersections from Cylindrical End Moduli Spaces
In this paper we present a way of computing a lower bound for genus of any smooth representative of a homology class of positive self-intersection in a smooth four-manifold X with second positive Betti number b+2 (X) = 1. We study the solutions of the Seiberg-Witten equations on the cylindrical end manifold which is the complement of the surface representing the class. The result can be formula...
متن کامل