Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-18T15:56:46.564Z Has data issue: false hasContentIssue false
  • English
  • Français

A formula for the Euler characteristic of line singularities on singular spaces

Published online by Cambridge University Press:  17 April 2009

Guangfeng Jiang
Guangfeng Jiang
Affiliation:
Department of Mathematics, Jinzhou Normal University, Jinzhou City, Liaoning 121000, Peoples Republic of China e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove an algebraic formula for the Euler characteristic of the Milnor fibres of functions with critical locus a smooth curve on a space which is a weighted homogeneous complete intersection with isolated singularity.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 335 - 343
Copyright
Copyright © Australian Mathematical Society 2000

References

REFERENCES

[1]Bruce, J.W. and Roberts, R.M., ‘Critical points of functions on analytic varieties’, Topology 27 (1988), 57–90.CrossRefGoogle Scholar
[2]Greuel, G.-M., Pfister, G. and Schoenemann, H., ‘Singular’, (A computer algebra system, ftp:[email protected] or http://www.mathematik.uni-kl.de).Google Scholar
[3]Jiang, G., Functions with non-isolated singularities on singular spaces, Thesis (Utrecht University, 1998).Google Scholar
[4]Jiang, G., Siersma, D., ‘Local embeddings of lines in singular hypersurfaces’, Ann. Inst. Fourier (Grenoble) 49 (1999), 1129–1147.Google Scholar
[5]Jiang, G. and Simis, A., ‘Higher relative primitive ideals’, Proc. Amer. Math. Soc. (to appear).Google Scholar
[6]Lê, D.T., ‘Ensembles analytiques complex avec lieu singulier de dimension un (d'après I.N. Iomdin)’, Publ. Math. Univ. Paris VII (1980), 87–94.Google Scholar
[7]Pellikaan, R., ‘Finite determinancy of functions with non-isolated singularities’, Proc. London Math. Soc 57 (1988), 357–382.CrossRefGoogle Scholar
[8]Pellikaan, R., Hypersurface singularities and resolutions of Jacobi modules, Thesis (Rijksuniversiteit Utrecht, 1985).Google Scholar
[9]Pellikaan, R., ‘Series of isolated singularities’, Contemp. Math 90 (1989), 241–259.Google Scholar
[10]Saito, K., ‘Theory of logarithmic differential forms and logarithmic vector fields’, J. Fac. Sci. Univ. Tokyo Sect 1A Math 27 (1980), 265–291.Google Scholar
[11]Seibt, P., ‘Differential filtrations and symbolic powers of regular primes’, Math. Z 166 (1979), 159–164.Google Scholar
[12]Tibăr, M., ‘Embedding non-isolated singularities into isolated singularities’, in Singularities, the Brieskorn anniversary volume, (Arnold, V.I., Greuel, G.-M., Steenbrink, J.H.M., Editors), Progress in Math. 162 (Birkhäuser Verlag, Boston MA, 1988), pp. 103–115.Google Scholar
[13]Wahl, J.M., ‘Derivations, automorphisms and deformations of quasi-homogeneous singularities’, in Singularities, Part 2 (Arcata, Calif., 1981), Proc. Sympos. Pure Math. 40 (Amer. Math. Soc., Providence, R.I., 1983), pp. 613–624.Google Scholar