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Desingularization in dimension 2

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References

  1. S. SBHYANKAR, Local uniformization on algebraic surfaces over ground fields of characteristic p ≠ 0. Ann. of Maths., 63 (1956), p. 491–526.

    Article  MathSciNet  Google Scholar 

  2. S. ABHYANKAR, On the ramification of algebraic functions, Ann. of Maths., 77 (1955), p. 575–592.

    MathSciNet  MATH  Google Scholar 

  3. S. ABHYANKAR, Reduction to multiplicity less than p in a p-cyclic extension of a two dimensional regular ring, Math. Ann. 154 (1964), 28–55

    Article  MathSciNet  MATH  Google Scholar 

  4. S. ABHYANKAR, Nonsplitting of valuations in extensions of two dimensional regular local domains, Math. Ann. 170 (1967), 87–144.

    Article  MathSciNet  MATH  Google Scholar 

  5. V. COSSART, Une nouvelle définition de l'invariant δ, Unpublished.

    Google Scholar 

  6. V. COSSART, Desingularization of embedded excellent surfaces. Tohoku Math. Journ. 33 (1981), 25–33.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. GIRAUD, Etude locale des singularités, Orsay, Pub. no. 26 (1972)

    Google Scholar 

  8. J. GIRAUD, Desingularization in low dimension, Lecture 2 in this volume.

    Google Scholar 

  9. H. HIRONAKA, Characteristic polyhedra of singularities, J. Math. Kyoto University, V. 7 (1967), 251–293.

    MathSciNet  MATH  Google Scholar 

  10. H. HIRONAKA, Bimeromorphic smoothing of a complex analytic space, University of Warwick (1967).

    Google Scholar 

  11. H. HIRONAKA, Introduction to the theory of infinitely near singular points, Memorias de Matematica del Instituto "Jorge Juan" 28.

    Google Scholar 

  12. H. HIRONAKA, Desingularization of excellent surfaces. Advanced Science Seminar in Algebraic Geometry (summer 1967). Notes by B.Bennett, Bowdoin College, reprinted in the appendix of this volume.

    Google Scholar 

  13. H. HIRONAKA, J.M. AROCA, J.U. VICENTE, The theory of the maximal contact. Memorias de Matematica del Instituto "Jorge Juan" 29.

    Google Scholar 

  14. H. HIRONAKA, Desingularization Theorems. Memorias de Matematica des Instituto "Jorge Juan" 30.

    Google Scholar 

  15. H.W.E. JUNG, Darstellung der Funktionen eines algebraischen Körpers zweier unabhängigen Veränderlichen in der Umgebung einer Stelle. J. Reine Angew. Math. 133 (1908), 289–314.

    MathSciNet  MATH  Google Scholar 

  16. J. LIPMAN, Desingularization of two-dimensional schemes. Ann. of Math. 107 (1978).

    Google Scholar 

  17. T. SANCHEZ, Teoria de singularidades de superficies algebroides sumergidas. Monografias y memorias de Matematica. IX, Pub del Instituto "Jorge Juan" de Matematicas. Madrid (1976).

    Google Scholar 

  18. O. ZARISKI, Exceptional singularities of an algebroid surface and their reduction. Atti. Acad. Naz. dei Lincei, serie VIII, vol. XLIII (1967), 135–146.

    MathSciNet  MATH  Google Scholar 

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© 1984 Springer-Verlag

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Cossart, V. (1984). Desingularization in dimension 2. In: Resolution of Surface Singularities. Lecture Notes in Mathematics, vol 1101. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072261

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  • DOI: https://doi.org/10.1007/BFb0072261

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  • Print ISBN: 978-3-540-13904-1

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