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Image multiple point spaces
and rectified homotopical depth


Author: Kevin Houston
Journal: Proc. Amer. Math. Soc. 126 (1998), 323-331
MSC (1991): Primary 14B15, 32S05; Secondary 32S60
DOI: https://doi.org/10.1090/S0002-9939-98-04446-3
MathSciNet review: 1459124
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Abstract: We investigate the local topology of multiple point spaces in the image of a finite complex analytic map. In particular, we find examples of maps for which the constant sheaf on an image multiple point space of the map is perverse. These results are proved by the use of a spectral sequence which calculates the homology of the image of a continuous map.


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  • [GM] V.V. Goryunov and D. Mond, Vanishing cohomology of singularities of mappings, Compositio Math., 89 (1993), 45-80. MR 94k:32058
  • [HL] H. Hamm and Lê D\~{u}ng Tráng, Rectified homotopical depth and Grothendieck Conjectures, in The Grothendieck Festschrift, Volume II, Progress in Mathematics 87, (Birkhäuser, Boston 1990), 311-351. MR 92j:32131
  • [Ho1] K. Houston, Local Topology of Images of Finite Complex Analytic Maps, Topology 36 (1997), 1077-1121. CMP 97:11
  • [Ho2] K. Houston, Global Topology of Images of Finite Complex Analytic Maps, to appear in the Mathematical Proceedings of the Cambridge Philosophical Society.
  • [L] Lê D\~{u}ng Tráng, Complex analytic functions with isolated singularities, J. Algebraic Geometry, 1 (1992), 83-100. MR 92j:32132
  • [M] R. MacPherson, Global questions in the topology of singular spaces, Proceedings of the International Congress of Mathematicians, Warsaw 1983, pp. 213-235. MR 86m:58016
  • [M] W.L. Marar, Mapping Fibrations, Manuscripta Mathematica, 80 (1993), 273-282. MR 94i:32058
  • [MM] W.L. Marar and D. Mond, Multiple point schemes for corank 1 maps, J. London Math. Soc. (2)39 (1989) 553-567. MR 91c:58010
  • [MP] D. Mond and R. Pellikaan, Fitting ideals and multiple points of analytic mappings, in Algebraic Geometry and Complex Analysis, ed. E. Ramirez de Arellano, Springer Lecture Notes in Mathematics 1414, Springer-Verlag, Berlin, 1990, 107-161. MR 91e:32035
  • [V] G. Valla, On determinantal ideals which are set-theoretic complete intersections, Compositio Mathematica, Vol 42 (1981), 3-11. MR 83g:14027
  • [W] C.T.C Wall, Finite determinacy of smooth map-germs, Bull. London Math. Soc., 13 (1981), 481-539. MR 83i:58020

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Additional Information

Kevin Houston
Affiliation: School of Mathematics and Statistics Middlesex University Bounds Green Road London N11 2NQ, United Kingdom
Email: k.houston@mdx.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-98-04446-3
Keywords: Image computing spectral sequence, image multiple point space, perverse sheaf, singularity
Received by editor(s): June 26, 1996
Communicated by: Ron Donagi
Article copyright: © Copyright 1998 American Mathematical Society

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