Pure homology of algebraic varieties

Article, Preprint English OPEN
Weber, Andrzej;
(2003)
  • Publisher: Elsevier BV
  • Journal: Topology,volume 43,issue 3,pages635-644 (issn: 0040-9383)
  • Publisher copyright policies & self-archiving
  • Related identifiers: doi: 10.1016/j.top.2003.09.001
  • Subject: Mathematics - Algebraic Topology | Geometry and Topology | Mathematics - Algebraic Geometry
    arxiv: Mathematics::K-Theory and Homology | Mathematics::Geometric Topology | Mathematics::Algebraic Topology | Mathematics::Symplectic Geometry

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 "image homology" for noncompl... View more
  • References (16)
    16 references, page 1 of 2

    [1] G. Barthel, J-P. Brasselet, K.-H. Fieseler, O. Gabber, L. Kaup: Rel`evement de cycles alg´ebriques et homomorphismes associ´es en homologie d'intersection. Ann. Math, 141 (1995), p. 147-179

    [2] A. Beilinson, J. Bernstein, P. Deligne: Faisceaux Pervers. Ast´erisque, 100 (1983)

    [3] A. Borel: Intersection cohomology, Progress in Mathematics, 50 (1984), Birkh¨auser

    [4] J. Cheeger, M. Goresky, R. MacPherson: L2-cohomology and intersection homology of singular algebraic varieties. Seminar on Differential Geometry, Ann. of Math. Stud., 102 (1982), Princeton Univ. Press, Princeton, N.J., p. 303-340

    [5] P. Deligne: Th´eorie de Hodge III. Publ. Math. I.H.E.S., 44 (1974), p. 5-77

    [6] M. Goresky, R. MacPherson: Intersection homology. Topology, 19 (1980), p. 135-162

    [7] M. Goresky, R. MacPherson: Intersection homology II. Invent. Math., 72 (1983), p. 77-130

    [8] F. Guillen: Une relation entre la filtration par le poids de Deligne et la filtration de Zeeman. Compositio Math., 61 (1987), no. 2, p. 201-227

    [9] H. C. King: Topological invariance of intersection homology without sheaves. Topology Appl., 20 (1985), no. 2, p. 149-160

    [10] C. McCrory: On the topology of Deligne's weight filtration. Singularities, Proc. Symp. Pure. Math., 40 (1983), part 2, p. 217-226

  • Metrics
Share - Bookmark