Algebraic cycles and intersection homology

Yokura, Shoji

doi:10.1090/S0002-9939-1988-0938641-X

Algebraic cycles and intersection homology
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Proc. Amer. Math. Soc. 103 (1988), 41-45 Request permission

Abstract:

We consider Dubson’s conjecture that the fundamental class in homology of an algebraic cycle on a complex algebraic variety is the image of a middle intersection homology class. In the case when the variety has only isolated singularities, we prove it for rational coefficients, and we give a counterexample to it for integral coefficients

References

-homologie d’intersection et faisceaux pervers

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
Mark Goresky and Robert MacPherson, Intersection homology. II, Invent. Math. 72 (1983), no. 1, 77–129. MR 696691, DOI 10.1007/BF01389130
M. Goresky and R. MacPherson, On the topology of complex algebraic maps, Algebraic geometry (La Rábida, 1981) Lecture Notes in Math., vol. 961, Springer, Berlin, 1982, pp. 119–129. MR 708330, DOI 10.1007/BFb0071279
Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. MR 507725
Kent W. Johnson, Immersion and embedding of projective varieties, Acta Math. 140 (1978), no. 1-2, 49–74. MR 463161, DOI 10.1007/BF02392303
John W. Milnor and James D. Stasheff, Characteristic classes, Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. MR 0440554
David Mumford, Algebraic geometry. I, Grundlehren der Mathematischen Wissenschaften, No. 221, Springer-Verlag, Berlin-New York, 1976. Complex projective varieties. MR 0453732