Image multiple point spaces and rectified homotopical depth

Houston, Kevin

doi:10.1090/S0002-9939-98-04446-3

Image multiple point spaces and rectified homotopical depth
HTML articles powered by AMS MathViewer

by Kevin Houston

Proc. Amer. Math. Soc. 126 (1998), 323-331

DOI: https://doi.org/10.1090/S0002-9939-98-04446-3

PDF | Request permission

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

Victor Goryunov and David Mond, Vanishing cohomology of singularities of mappings, Compositio Math. 89 (1993), no. 1, 45–80. MR 1248891
Helmut A. Hamm and Lê Dũng Tráng, Rectified homotopical depth and Grothendieck conjectures, The Grothendieck Festschrift, Vol. II, Progr. Math., vol. 87, Birkhäuser Boston, Boston, MA, 1990, pp. 311–351. MR 1106902
K. Houston, Local Topology of Images of Finite Complex Analytic Maps, Topology 36 (1997), 1077–1121.
K. Houston, Global Topology of Images of Finite Complex Analytic Maps, to appear in the Mathematical Proceedings of the Cambridge Philosophical Society.
Lê Dũng Tráng, Complex analytic functions with isolated singularities, J. Algebraic Geom. 1 (1992), no. 1, 83–99. MR 1129840
Robert MacPherson, Global questions in the topology of singular spaces, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 213–235. MR 804683
W. L. Marar, Mapping fibrations, Manuscripta Math. 80 (1993), no. 3, 273–281. MR 1240650, DOI 10.1007/BF03026553
Washington Luiz Marar and David Mond, Multiple point schemes for corank $1$ maps, J. London Math. Soc. (2) 39 (1989), no. 3, 553–567. MR 1002466, DOI 10.1112/jlms/s2-39.3.553
David Mond and Ruud Pellikaan, Fitting ideals and multiple points of analytic mappings, Algebraic geometry and complex analysis (Pátzcuaro, 1987) Lecture Notes in Math., vol. 1414, Springer, Berlin, 1989, pp. 107–161. MR 1042359, DOI 10.1007/BFb0090254
Giuseppe Valla, On determinantal ideals which are set-theoretic complete intersections, Compositio Math. 42 (1980/81), no. 1, 3–11. MR 594479
C. T. C. Wall, Finite determinacy of smooth map-germs, Bull. London Math. Soc. 13 (1981), no. 6, 481–539. MR 634595, DOI 10.1112/blms/13.6.481