Vanishing cohomology of singularities of mappings
Goryunov, Victor ; Mond, David
Compositio Mathematica, Tome 89 (1993), p. 45-80 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1993-01-01
@article{CM_1993__89_1_45_0,
     author = {Goryunov, Victor and Mond, David},
     title = {Vanishing cohomology of singularities of mappings},
     journal = {Compositio Mathematica},
     volume = {89},
     year = {1993},
     pages = {45-80},
     mrnumber = {1248891},
     zbl = {0839.32017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1993__89_1_45_0}
}

Goryunov, Victor; Mond, David. Vanishing cohomology of singularities of mappings. Compositio Mathematica, Tome 89 (1993) pp. 45-80. http://gdmltest.u-ga.fr/item/CM_1993__89_1_45_0/

[0] P. Deligne, Théorie de Hodge II, Publications Mathématiques de l'I.H.E.S. 40 (1971) 5-58. | Numdam | MR 498551 | Zbl 0219.14007

[1] P. Deligne, Théorie de Hodge III, Publications Mathématiques de l'I.H.E.S. 44 (1972) 5-77. | Numdam | MR 498552 | Zbl 0237.14003

[2] I. Dolgachev, Weighted Projective Varieties, Lecture Notes in Math. 956, Springer Verlag, Berlin (1982) 34-71. | MR 704986 | Zbl 0516.14014

[3] R. Godement, Topologie Algébrique et Théorie des Faisceaux, Hermann, Paris, 1964. | MR 345092

[4] V.V. Goryunov, Singularities of projections of complete intersections, Vol 22 of VINITI series "Sovremennye Problemy Matematiki, Noveishye Dostizeniya" (in Russian), Moscow, 1983, 130-166. | MR 735443

[5] V.V. Goryunov, Semi-simplicial resolutions and the homology of images and discriminants of mappings, preprint, University of Warwick, 1992. | MR 1309234 | Zbl 0821.32032

[6] G.-M. Greuel, Der Gauss-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten, Math. Ann. 217 (1975) 235-266. | MR 396554 | Zbl 0285.14002

[7] G.-M. Greuel and H.A. Hamm, Invarianten quasihomogener vollständigen Durchschnitten, Invent. Math. 49 (1978) 67-86. | MR 511096 | Zbl 0394.32006

[8] R.C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice Hall, Englewood Cliffs, 1965. | MR 180696 | Zbl 0141.08601

[9] H.A. Hamm, Lokale topologische Eigenschaften komplexer Räume, Math. Ann. 191 (1971) 235-252. | MR 286143 | Zbl 0214.22801

[10] H.A. Hamm, Zum Homotopietyp Steinscher Räume, J. Reine und Angew. Math. 338 (1983) 121-135. | MR 684017 | Zbl 0491.32010

[11] H.A. Hamm, Invariants of weighted homogeneous singularities, Journées Complexes, 1985 (Nancy, 1985) 6-13. | MR 933782 | Zbl 0659.32012

[12] S.L. Kleiman, Multiple point formulae I: Iteration, Acta Math. 47 (1981) 13-49. | MR 631086 | Zbl 0479.14004

[13] D.T. Lê, Le concept de singularité isolée de fonction analytique, Adv. Studies in Pure Math. 8 (1986) 215-227. | MR 894295 | Zbl 0656.32005

[14] D.T. Lê, Complex analytic functions with isolated singularities, preprint, 1991.

[15] E.J.N. Looijenga, Isolated singular points on complete intersections, Lecture Notes in Maths. 77, London Math. Soc. 1984. | MR 747303 | Zbl 0552.14002

[16] W.L. Marar, The Euler characteristic of the disentanglement of the image of a corank 1 map-germ, in Singularity Theory and Applications, Warwick 1989, D. Mond and J. Montaldi (eds.), Lecture Notes in Math. 1462, Springer Verlag, Berlin, Heidelberg, New York, 1991. | MR 1129034 | Zbl 0734.58013

[17] W.L. Marar, Thesis, University of Warwick, 1989.

[18] W.L. Marar, Mapping fibrations, to appear. | MR 1240650

[19] W.L. Marar and D. Mond, Multiple point schemes for corank 1 maps, J. London Math. Soc. (2)39 (1989) 553-567. | MR 1002466 | Zbl 0691.58015

[20] J.N. Mather, Stability of C∞ Mappings VI: The Nice Dimensions, Proc. Liverpool Singularities Symposium, Lecture Notes in Math. 192, Springer Verlag, Berlin, 1971, 207-253. | Zbl 0211.56105

[21] J.P. May, Simplicial Objects in Algebraic Topology, University of Chicago Press, 1967. | MR 222892

[22] D. Mond, On the classification of germs of maps from R2 to R3, Proc. London Math. Soc. (3) 50 (1985) 333-369. | MR 772717 | Zbl 0557.58006

[23] D. Mond, The number of vanishing cycles in a quasihomogeneous mapping C2 → C3, Quarterly Journal of Math. (Oxford), (2)42 (1991) 335-345. | Zbl 0764.32013

[24] D. Mond, Vanishing cycles for analytic maps, in D. Mond and J. Montaldi (eds.), Singularity Theory and Applications, Warwick 1989, Lecture Notes in Math. 1462, Springer Verlag, Berlin, Heidelberg, New York, 1991. | MR 1129035 | Zbl 0723.00028

[25] R. Peine and F. Ronga, A geometric approach to the arithmetic genus of a projective manifold of dimension 3, Topology 20 (1981) 179-190. | MR 605657 | Zbl 0463.14012

[26] L. Solomon, Invariants of finite reflection groups, Nagoya Math. J. 22 (1963), No. 1, 57-64. | MR 154929 | Zbl 0117.27104

[27] J.H.M. Steenbrink, Mixed Hodge Theory on the Vanishing Cohomology, in Per Holm, (ed.), Real and Complex Singularities, Oslo 1976, Sijthoff and Noordhoff, Alphen aan den Rijn (1977) 525-563. | MR 485870 | Zbl 0373.14007

[28] J.H.M. Steenbrink, Mixed Hodge Theory, manuscript of book (in preparation).

[29] C.T.C. Wall, A note on symmetry of singularities, Bull. London Math. Soc. 12 (1980) 169-175. | MR 572095 | Zbl 0427.32010

[30] C.T.C. Wall, Finite determinacy of smooth map-germs, Bull. London Math. Soc. 13 (1981) 481-539. | MR 634595 | Zbl 0451.58009