Acta Mathematica

, Volume 181, Issue 1, pp 109–158 | Cite as

Good points and constructive resolution of singluarities

  • S. Encinas
  • O. Villamayor
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Ab1]Abhyankar, S.S., Good points of a hypersurface.Adv. in Math., 68 (1988), 87–256MATHMathSciNetCrossRefGoogle Scholar
  2. [Ab2]Abhyankar, S.S., Analytic desingularization in characteristic zero. Preprint, 1996Google Scholar
  3. [AHV1]Aroca, J.M., Hironaka, H., &Vicente, J.L.,The Theory of Maximal Contact. Memorias de Matemática del Instituto Jorge Juan, 29, Consejo Superior de Investigaciones Científicas, Madrid, 1975.Google Scholar
  4. [AHV2]-—,Desingularization Theorems, Memorias de Matemática del Instituto Jorge Juan, 30. Consejo Superior de Investigaciones Científicas, Madrid, 1977.MATHGoogle Scholar
  5. [AJ]Abramovich, D. &Jong, A.J. ed, Smoothness, semistability and toroidal geometry.J. Algebraic Geom., 6 (1997), 789–801.MATHMathSciNetGoogle Scholar
  6. [AW]Abramovich, D. &Wang, J., Equivariant resolution of singularities in characteristic O.Math. Res. Lett., 4 (1997), 427–433.MATHMathSciNetGoogle Scholar
  7. [Ben]Bennett, B. M., On the characteristic function of a local ring.Ann. of Math. 91 (1970), 25–87.MATHMathSciNetCrossRefGoogle Scholar
  8. [Ber]Berthelot, P., Altérations des variétés algébriques (d'après A. J. de Jong), inSéminaire Bourbaki, vol. 1995/96, exp. no 815.Astérisque, 241 (1997), 273–311.Google Scholar
  9. [BM1]Bierstone, E., &Milman, P., A simple constructive proof of canonical resolution of singularities, inEffective Methods in Algebraic Geometry (Castiglioncello, 1990), pp. 11–30. Progr. Math., 94. Birkhäuser, Boston, MA, 1991.Google Scholar
  10. [BM2]-— Canonical desingularization in characteristic zero by blowing up the maximal strata of a local invariant.Invent. Math., 128 (1997), 207–302.MATHMathSciNetCrossRefGoogle Scholar
  11. [BP]Bogomolov, F. &Pantev, T., Weak Hironaka theorem.Math. Res. Lett., 3 (1996), 299–307.MATHMathSciNetGoogle Scholar
  12. [Ca]Cano, F.,Desingularización de Superficies. Seminario Iberoamericano de Matemáticas (Singularidades en Tordesillas), Fascículo 1. Valladolid, 1995.Google Scholar
  13. [CGO]Cossart, V., Giraud, J. &Orbanz, U.,Resolutions of Surface Singularities. Lecture Notes in Math., 1101. Springer-Verlag, Berlin-New York, 1984.Google Scholar
  14. [E]Encinas, S., Resolución constructiva de singluaridades de familias de esquemas. Ph.D. Thesis, Universidad de Valladolid, 1996.Google Scholar
  15. [EV]Encinas, S. & Villamayor, O., Constructive desingularization and equivariance: Introductory notes, inWorking Week on Mountains and Singularities (Obergurgl, 1997).Google Scholar
  16. [G1]Giraud, J.,Étude locale des singularités. Publ. Math. Orsay, 26. U.E.R. Mathématique, Université Paris XI, Orsay, 1972.MATHGoogle Scholar
  17. [G2]-— Sural théorie du contact maximal.Math. Z., 137 (1974), 285–310.MATHMathSciNetCrossRefGoogle Scholar
  18. [G3]-— Contact maximal en caractéristique positive.Ann. Sci. École Norm. Sup. (4) 8 (1975), 201–234.MATHMathSciNetGoogle Scholar
  19. [G4]-— Remarks on desingularization problems.Nova Acta Leopoldina, 52 (240) (1981), 103–107.MATHMathSciNetGoogle Scholar
  20. [Ha]Hartshorne, R.,Algebraic Geometry, Graduate Texts in Math., 52. Springer-Verlag, New York, 1983.Google Scholar
  21. [Hi1]Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero, I; II.Ann. of Math., 79 (1964), 109–203; 205–326.MATHMathSciNetCrossRefGoogle Scholar
  22. [Hi2]-— Idealistic exponents of singularity, inAlgebraic Geometry (Baltimore, MD, 1976), pp. 52–152. John Hopkins Univ. Press, Baltimore, MD, 1977.Google Scholar
  23. [HIO]Herrmann, M., Ikeda, S. &Orbanz, U.,Equimultiplicity and Blowing Up. Springer-Verlag, Berlin-New York, 1988.MATHGoogle Scholar
  24. [J]Jong, A. J. de, Smoothness, semi-stability and alterations. Preprint 916, University of Utrecht, 1995.Google Scholar
  25. [LT1]Lejeune-Jalabert, M. &Teissier, B., Normal cones and sheaves of relative jets.Compositio Math., 28 (1974), 305–331.MATHMathSciNetGoogle Scholar
  26. [LT2]Lejeune-Jalabert, M. Quelques calculs utiles pour la résolution des singularités. Centre de Mathématiques de l'École Polytechnique, 1971.Google Scholar
  27. [M]Moh, T. T., Canonical uniformization of hypersurface singularities of characteristic zero.Camm. Algebra 20 (1992), 3207–3251.MATHMathSciNetGoogle Scholar
  28. [O]Oda, T., Infinitely very near-singularity points (complex analytic singularities).Adv. Stud. Pure. Math., 8 (1986), 363–404.MathSciNetGoogle Scholar
  29. [S]Spivakovsky, M., Resolution of singularities, inJournées singulières et jacobiennes. Institut Fourier, Grenoble, 1996.Google Scholar
  30. [V1]Villamayor, O., Constructiveness of Hironaka's resolution.Ann. Sci. École Norm. Sup. (4) 22 (1989), 1–32.MATHMathSciNetGoogle Scholar
  31. [V2]-—, Patching local uniformizations.Ann. Sci. École Norm. Sup. (4) 25 (1992), 629–677.MATHGoogle Scholar
  32. [V3]-—, On good points and a new canonical algorithm of resolution of singularities, inReal Analytic and Algebraic Geometry (Trento, 1992), pp. 277–291. de Gruyter, Berlin-New York, 1995.Google Scholar
  33. [V4]-—, Introduction to the algorithm of resolution, inAlgebraic Geometry and Singularities (La Rábida, 1991), pp. 123–154. Progr. Math., 134. Birkhäuser, Basel, 1996.Google Scholar
  34. [Z]Zariski, O., Local uniformization on algebraic varieties.Ann. of Math., 41 (1940), 852–860.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Institut Mittag-Leffler 1998

Authors and Affiliations

  • S. Encinas
    • 1
  • O. Villamayor
    • 2
  1. 1.Departamento de Matemática Aplicada F. E. T. S. Arquitectura Universidad de ValladolidUniversidad de ValladolidValladolidSpain
  2. 2.Universidad Autonoma de. Madrid Departamento de MatemáticasCiudad Universitaria de Canto BlancoMadridSpain

Personalised recommendations