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Integral closure of modules and Whitney equisingularity

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References

  1. Brodersen, H.: On finite and infiniteC k A determinacy. Preprint, University of Oslo, vol. 14 part 1 and 2, 1984

  2. Damon, J.N.: Topological invariants of μ-constant deformations of complete intersection singularities. Q. J. Math., Oxf. II. Ser.40, 139–160 (1989)

    Google Scholar 

  3. Damon, J.N., Gaffney, T.: Topological triviality of deformations of functions and Newton filtrations. Invent. Math.72, 335–358 (1983)

    Google Scholar 

  4. Fitting, H.: Die Determinantenideale einer Modulo Jahresler. Jahresber. Dtsch. Math. Ver.46, 195–220 (1936)

    Google Scholar 

  5. Gaffney, T.: Polar multiplicities and equisingularity of map germs. Topology (to appear)

  6. Gaffney, T.: Multiplicities and equisingularity of ICIS germs. (in preparation)

  7. Gaffney, T.: Hilbert schemes, integral closure and finite ℒ0-determinacy. (in preparation)

  8. Hironaka, H.: Introduction to real-analytic sets and real analytic maps. Publ. Inst. Mat. “L. Tonelli” dell'Univérsita di Pisa, Pisa 1973

    Google Scholar 

  9. Kuo, T.C.: The ratio test for analytic Whitney stratifications, In: Wall, C.T.C. (ed.) Proceedings of the Liverpool Singularities Symposium I. (Lect. Note Math., vol. 192, pp. 141–149) Berlin Heidelberg New York: Springer 1971

    Google Scholar 

  10. Looijenga, E.J.N.: Isolated singular points on complete intersections (Lond. Math. Soc. Lect. Note Ser., vol. 77) Cambridge: Cambridge University Press 1984

    Google Scholar 

  11. Mather, J.N.: Stability ofC ∞-mappings: I The division theorem. Ann. Math,87, 87–104 (1968)

    Google Scholar 

  12. Mather, J.N.: II Infinitesimal stability implies stability. Ann. Math.89, 259–291 (1969)

    Google Scholar 

  13. Mather, J.N.: III Finitely determined map-germs. Publ. Math., Inst. Hautes Étud. Sci.35, 127–156 (1969)

    Google Scholar 

  14. Mather, J.N.: IV Classification of stable germs by ℝ algebras. Publ. Math., Inst. Hautes Étud. Sci.37, 223–248 (1970)

    Google Scholar 

  15. Mather, J.N.: V Transversality. Adv. Math.4, 301–335 (1970)

    Google Scholar 

  16. Mather, J.N.: VI The nice dimensions In: Proceedings of the Liverpool Singularities Symposium I. (Lect. Notes Math., vol. 192, pp. 207–255) Berlin Heidelberg New York: Springer 1971

    Google Scholar 

  17. Oka, M.: Principal Zeta-Function of non-degenerate complete intersection singularity. Preprint, Tokyo Institute of Technology 1988

  18. Rees, D.: Reduction of modules. Math. Proc. Camb. Philos. Soc.101, 431–449 (1987)

    Google Scholar 

  19. Teissier, B.: Cycles évanescents sections planes et conditions de Whitney. Singularités à Cargèsse. (Astérisque, vols. 7–8, pp. 285–362), Paris: Soc. Math. Fr. 1973

    Google Scholar 

  20. Teissier, B.: Multiplicities polaires, sections planes, et conditions de Whitney. In: Aroca, J.M. et al. (eds.) Algebraic Geometry. La Rabida 1981 (Lect. Notes Math., vol. 961, pp. 314–491) Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  21. Teissier, B.: Introduction to equisingularity problems. In: Hartshorne, (ed.) Algebraic Geometry. Arcata 1974. (Proc. Symp. Pure Math., vol. 29) Providence, RI: Am. Math. Soc. 1975

    Google Scholar 

  22. Teissier, B.: The hunting of invariants in the geometry of discriminants. In: Holm, P. (ed.) Real and complex singularities. Proc. Nordic Summer School, Oslo 1976. Alphen on den Rijn: Sijthoff and Noordhoff 1977

    Google Scholar 

  23. Thom, R., Levine, H.: Singularities of differentiable mappings. Notes, University of Bonn. (Lect. Notes Math., vol. 192, pp. 1–89) Berlin Heidelberg New York: Springer 1971

    Google Scholar 

  24. Wall, C.T.C.: Finite determinancy of smooth map-germs. Bull. Lond. Math. Soc.13, 481–539 (1981)

    Google Scholar 

  25. Wilson, L.: Infinitely determined map-germs. Can. J. Math.33 (no 3) 671–684 (1981)

    Google Scholar 

  26. Khovanskii, A.G.: Newton polyhedra and toroidal varieties. Funct. Anal. Appl.11, 289–295 (1977)

    Google Scholar 

  27. Verdier, J.L.: Stratifications de Whitney et théorème de Bertini-Sard. Invent. Math.136, 295–312 (1976)

    Google Scholar 

  28. Brumfiel, G.W.: Real valuation rings and ideals. In: Géométrie Algébrique Réelle et Formes Quadratiques. Rennes 1981. (Lect. Notes Math., vol. 959, pp. 55–97) Berlin Heidelberg New York: Springer 1982

    Google Scholar 

  29. Lejeune-Jalabert, M., Teissier, B.: Dependence integrale sur les ideux et equisingularite. Publ. Inst. Fourier, St. Martin d'Heres F-38402, 1975

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Northeastern University, 02115, Boston, MA, USA

    Terence Gaffney

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  1. Terence Gaffney
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Oblatum 4-II-1991 & 3-VI-1991

Supported in part by NSF Grants DMS-8803478, INT-887075

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Gaffney, T. Integral closure of modules and Whitney equisingularity. Invent Math 107, 301–322 (1992). https://doi.org/10.1007/BF01231892

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