Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant

Inventiones Mathematicae

Volumn 128, Issue 2, 1997, Pages 207-302

  Bierstone, Edward ^a   Milman, Pierre D ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031486450     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050141     Document Type: Article

References (31)

1. Abhyankar, S.S.: Weighted expansions for canonical desingularization (Lect. Notes Math., Vol. 910) Berlin Heidelberg New York: Springer 1982
2. Abhyankar, S.S.: Good points of a hypersurface. Adv. in Math. 68, 87-256 (1988)
3. Aroca, J.M., Hironaka, H., Vicente, J.L.: The theory of the maximal contact (Mem. Math. Inst. Jorge Juan, No. 29) Madrid: Consejo Superior de Investigaciones Científicas 1975
4. Aroca, J.M., Hironaka, H., Vicente, J.L.: Desingularization theorems, (Mem. Math. Inst. Jorge Juan, No. 30) Madrid: Consejo Superior de Investigaciones Científicas 1977
5. Artin, M.: Algebraic spaces (Yale Math. Monographs, No. 3) New Haven: Yale University Press 1971
6. Bennett, B.M.: On the characteristic function of a local ring. Ann. of Math. (2) 91, 25-87 (1970)
7. Berkovich, V.G.: Spectral theory and analytic geometry over non-Archimedean fields (Math. Surveys and Monographs, No. 33) Providence: Amer. Math. Soc. 1990
8. Bierstone, E., Milman, P.D.: Relations among analytic functions I, II. Ann. Inst. Fourier (Grenoble) 37 (1), 187-239 (1987), 37 (2), 49-77 (1987)
9. Bierstone, E., Milman, P.D.: Relations among analytic functions I, II. Ann. Inst. Fourier (Grenoble) 37 (1), 187-239 (1987), 37 (2), 49-77 (1987)
10. Bierstone, E., Milman, P.D.: Local analytic invariants and splitting theorems in differential analysis. Israel J. Math. 60, 257-280 (1987)
11. Bierstone, E., Milman, P.D.: Semianalytic and subanalytic sets. Publ. Math. I.H.E.S. 67, 5-42 (1988)
12. Bierstone, E., Milman, P.D.: Uniformization of analytic spaces. J. Amer. Math. Soc. 2, 801-836 (1989)
13. Bierstone, E., Milman. P.D.: Arc-analytic functions. Invent. Math. 101, 411-424 (1990)
14. Bierstone, E., Milman, P.D.: A simple constructive proof of canonical resolution of singularities. In: Effective methods in algebraic geometry (Progress in Math., Vol. 94, pp. 11-30) Boston: Birkhäuser 1991
15. Dyn'kin E.M.: Pseudoanalytic extensions of smooth functions. The uniform scale. Amer. Math. Soc. Translations (2) 115, 33-58 (1980)
16. Giraud, J.: Sur la théorie du contact maximal. Math. Z. 137, 285-310 (1974)
17. Grothendieck, A., Dieudonné, J.A.: Eléments de géométrie algébrique I. Berlin Heidelberg New York: Springer 1971
18. Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero: I, II. Ann. of Math. (2) 79, 109-326 (1964)
19. Hironaka, H.: Introduction to the theory of infinitely near singular points (Mem. Math. Inst. Jorge Juan, No. 28) Madrid: Consejo Superior de Investigaciones Cientificas 1974
20. Hironaka, H.: Idealistic exponents of singularity. In: Algebraic geometry, J.J. Sylvester Sympos., Johns Hopkins Univ., Baltimore 1976, pp. 52-125. Baltimore: Johns Hopkins Univ. Press 1977
21. de Jong, A.J.: Smoothness, semi-stability and alterations (preprint, 1995)
22. Knutson, D.: Algebraic spaces (Lect. Notes Math., Vol. 203) Berlin Heidelberg New York: Springer 1971
23. Lejeune-Jalabert, M., Teissier, B.: Dépendence intégrale sur les idéaux et équisingularité. (Séminaire Ecole Polytechnique 1974) St. Martin d'Hères: Inst. Fourier 1975
24. Lipman, J.: Introduction to resolution of singularities. In: Algebraic geometry, Arcata 1974 (Proc. Sympos. Pure Math., Vol. 29, pp. 187-230) Providence: Amer. Math. Soc. 1975
25. Lojasiewicz, S.: Sur les trajectoires du gradient d'une fonction analytique. Univ. Stud. Bologna Sem. Geom. 1982-83, 115-117 (1983)
26. Moh, T.T.: Quasi-canonical uniformization of hypersurface singularities of characteristic zero. Comm. Alg. 20, 3207-3249 (1992)
27. Serre, J.-P.: Lie algebras and Lie groups. New York Amsterdam: Benjamin 1965
28. Spivakovsky, M.: Resolution of singularities (preprint)
29. e série) 22, 1-32 (1989)
30. e série) 25, 629-677 (1992)
31. Youssin, B.: Newton polyhedra without coordinates. Newton polyhedra of ideals (Mem. Amer. Math. Soc., No. 433) Providence: Amer. Math. Soc. 1990