Vanishing cohomology of singularities of mappings

Victor Goryunov; David Mond

Compositio Mathematica (1993)

  • Volume: 89, Issue: 1, page 45-80
  • ISSN: 0010-437X

How to cite

top

Goryunov, Victor, and Mond, David. "Vanishing cohomology of singularities of mappings." Compositio Mathematica 89.1 (1993): 45-80. <http://eudml.org/doc/90252>.

@article{Goryunov1993,
author = {Goryunov, Victor, Mond, David},
journal = {Compositio Mathematica},
keywords = {vanishing cohomology; singularities of mappings; mixed Hodge structure},
language = {eng},
number = {1},
pages = {45-80},
publisher = {Kluwer Academic Publishers},
title = {Vanishing cohomology of singularities of mappings},
url = {http://eudml.org/doc/90252},
volume = {89},
year = {1993},
}

TY - JOUR
AU - Goryunov, Victor
AU - Mond, David
TI - Vanishing cohomology of singularities of mappings
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 89
IS - 1
SP - 45
EP - 80
LA - eng
KW - vanishing cohomology; singularities of mappings; mixed Hodge structure
UR - http://eudml.org/doc/90252
ER -

References

top
  1. [0] P. Deligne, Théorie de Hodge II, Publications Mathématiques de l'I.H.E.S.40 (1971) 5-58. Zbl0219.14007MR498551
  2. [1] P. Deligne, Théorie de Hodge III, Publications Mathématiques de l'I.H.E.S.44 (1972) 5-77. Zbl0237.14003MR498552
  3. [2] I. Dolgachev, Weighted Projective Varieties, Lecture Notes in Math.956, Springer Verlag, Berlin (1982) 34-71. Zbl0516.14014MR704986
  4. [3] R. Godement, Topologie Algébrique et Théorie des Faisceaux, Hermann, Paris, 1964. MR345092
  5. [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. MR735443
  6. [5] V.V. Goryunov, Semi-simplicial resolutions and the homology of images and discriminants of mappings, preprint, University of Warwick, 1992. Zbl0821.32032MR1309234
  7. [6] G.-M. Greuel, Der Gauss-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten, Math. Ann.217 (1975) 235-266. Zbl0285.14002MR396554
  8. [7] G.-M. Greuel and H.A. Hamm, Invarianten quasihomogener vollständigen Durchschnitten, Invent. Math.49 (1978) 67-86. Zbl0394.32006MR511096
  9. [8] R.C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice Hall, Englewood Cliffs, 1965. Zbl0141.08601MR180696
  10. [9] H.A. Hamm, Lokale topologische Eigenschaften komplexer Räume, Math. Ann.191 (1971) 235-252. Zbl0214.22801MR286143
  11. [10] H.A. Hamm, Zum Homotopietyp Steinscher Räume, J. Reine und Angew. Math.338 (1983) 121-135. Zbl0491.32010MR684017
  12. [11] H.A. Hamm, Invariants of weighted homogeneous singularities, Journées Complexes, 1985 (Nancy, 1985) 6-13. Zbl0659.32012MR933782
  13. [12] S.L. Kleiman, Multiple point formulae I: Iteration, Acta Math.47 (1981) 13-49. Zbl0479.14004MR631086
  14. [13] D.T. Lê, Le concept de singularité isolée de fonction analytique, Adv. Studies in Pure Math.8 (1986) 215-227. Zbl0656.32005MR894295
  15. [14] D.T. Lê, Complex analytic functions with isolated singularities, preprint, 1991. 
  16. [15] E.J.N. Looijenga, Isolated singular points on complete intersections, Lecture Notes in Maths.77, London Math. Soc.1984. Zbl0552.14002MR747303
  17. [16] W.L. Marar, The Euler characteristic of the disentanglement of the image of a corank 1 map-germ, in Singularity Theory and Applications, Warwick1989, D. Mond and J. Montaldi (eds.), Lecture Notes in Math.1462, Springer Verlag, Berlin, Heidelberg, New York, 1991. Zbl0734.58013MR1129034
  18. [17] W.L. Marar, Thesis, University of Warwick, 1989. 
  19. [18] W.L. Marar, Mapping fibrations, to appear. MR1240650
  20. [19] W.L. Marar and D. Mond, Multiple point schemes for corank 1 maps, J. London Math. Soc. (2)39 (1989) 553-567. Zbl0691.58015MR1002466
  21. [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. Zbl0211.56105
  22. [21] J.P. May, Simplicial Objects in Algebraic Topology, University of Chicago Press, 1967. MR222892
  23. [22] D. Mond, On the classification of germs of maps from R2 to R3, Proc. London Math. Soc. (3) 50 (1985) 333-369. Zbl0557.58006MR772717
  24. [23] D. Mond, The number of vanishing cycles in a quasihomogeneous mapping C2 → C3, Quarterly Journal of Math. (Oxford), (2)42 (1991) 335-345. Zbl0764.32013
  25. [24] D. Mond, Vanishing cycles for analytic maps, in D. Mond and J. Montaldi (eds.), Singularity Theory and Applications, Warwick1989, Lecture Notes in Math.1462, Springer Verlag, Berlin, Heidelberg, New York, 1991. Zbl0723.00028MR1129035
  26. [25] R. Peine and F. Ronga, A geometric approach to the arithmetic genus of a projective manifold of dimension 3, Topology20 (1981) 179-190. Zbl0463.14012MR605657
  27. [26] L. Solomon, Invariants of finite reflection groups, Nagoya Math. J.22 (1963), No. 1, 57-64. Zbl0117.27104MR154929
  28. [27] J.H.M. Steenbrink, Mixed Hodge Theory on the Vanishing Cohomology, in Per Holm, (ed.), Real and Complex Singularities, Oslo1976, Sijthoff and Noordhoff, Alphen aan den Rijn (1977) 525-563. Zbl0373.14007MR485870
  29. [28] J.H.M. Steenbrink, Mixed Hodge Theory, manuscript of book (in preparation). 
  30. [29] C.T.C. Wall, A note on symmetry of singularities, Bull. London Math. Soc.12 (1980) 169-175. Zbl0427.32010MR572095
  31. [30] C.T.C. Wall, Finite determinacy of smooth map-germs, Bull. London Math. Soc.13 (1981) 481-539. Zbl0451.58009MR634595

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.