Intersection homology Betti numbers

Durfee, Alan H.

doi:10.1090/S0002-9939-1995-1233968-2

Intersection homology Betti numbers
HTML articles powered by AMS MathViewer

by Alan H. Durfee

Proc. Amer. Math. Soc. 123 (1995), 989-993

DOI: https://doi.org/10.1090/S0002-9939-1995-1233968-2

PDF | Request permission

Abstract:

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.

References

A. A. Beĭlinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces, I (Luminy, 1981) Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171 (French). MR 751966
P. Bressler, M. Finkelberg, and V. Lunts, Vanishing cycles on Grassmannians, Duke Math. J. 61 (1990), no. 3, 763–777. MR 1084458, DOI 10.1215/S0012-7094-90-06128-9
Pierre Deligne, Théorie de Hodge. II, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 5–57 (French). MR 498551
Alan H. Durfee and Morihiko Saito, Mixed Hodge structures on the intersection cohomology of links, Compositio Math. 76 (1990), no. 1-2, 49–67. Algebraic geometry (Berlin, 1988). MR 1078857
Jonathan Fine and Prabhakar Rao, On intersection homology at isolated singularities, Algebras Groups Geom. 5 (1988), no. 4, 329–340. MR 1104296
Mark Goresky and Robert MacPherson, Intersection homology theory, Topology 19 (1980), no. 2, 135–162. MR 572580, DOI 10.1016/0040-9383(80)90003-8

Morse theory and intersection homology

101

Morihiko Saito, Mixed Hodge modules, Publ. Res. Inst. Math. Sci. 26 (1990), no. 2, 221–333. MR 1047415, DOI 10.2977/prims/1195171082
Morihiko Saito, Mixed Hodge modules and applications, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990) Math. Soc. Japan, Tokyo, 1991, pp. 725–734. MR 1159259