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Image multiple point spaces and rectified homotopical depth
Author(s):
Kevin
Houston
Journal:
Proc. Amer. Math. Soc.
126
(1998),
323-331.
MSC (1991):
Primary 14B15, 32S05;
Secondary 32S60
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.
References:
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- 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
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- 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
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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:
10.1090/S0002-9939-98-04446-3
PII:
S 0002-9939(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
Copyright of article:
Copyright
1998,
American Mathematical Society
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