Book Review
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MathSciNet review:
1567680
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Book Information:
Author:
Oscar Zariski
Title:
Le problème des modules pour les branches planes
Additional book information:
with an appendix by Bernard Teissier. Hermann, Paris, 1986, 209 pp., $28.00. ISBN 2-7065-6036-4.
1. K. Brauner, Zur Geometrie der Funktionen zweier complexen Veränderlichen, III, IV, Abh. Math. Sem. Hamburg 6 (1928), 8-54.
Werner Burau, Wilhelm Blaschkes Leben und Werk, Mitt. Math. Ges. Hamburg 9 (1963), no. 2, 24–40 (1963) (German). MR 0166066
Charles Delorme, Sur la dimension d’un espace de singularités, C. R. Acad. Sci. Paris Sér. A-B 280 (1975), Aii, A1287–A1289. MR 437544
David Eisenbud and Walter Neumann, Three-dimensional link theory and invariants of plane curve singularities, Annals of Mathematics Studies, vol. 110, Princeton University Press, Princeton, NJ, 1985. MR 817982
5. F. Enriques and O. Chisini, Lezioni sulla theorie geometrica delle equazioni e delle funzioni algebriche, 3 vols., Bologna, 1915, 1918, and 1925.
Erich Hecke, Lectures on the theory of algebraic numbers, Graduate Texts in Mathematics, vol. 77, Springer-Verlag, New York-Berlin, 1981. Translated from the German by George U. Brauer, Jay R. Goldman and R. Kotzen. MR 638719
7. M. Lejeune and B. Teissier, Clôture integrale des ideaux et équisingularité, Sém. École Polytechnique, (1973-1974).
John Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies, No. 61, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. MR 0239612
9. H. C. Pinkham, Deformations of algebraic varieties with G, Astérisque 20 (1974).
J. G. Semple and G. T. Kneebone, Algebraic curves, Oxford University Press, London-New York, 1959. MR 0124801
Sherwood Washburn, Analytically trivial families of local rings, J. Algebra 35 (1975), 528–533. MR 371890, DOI 10.1016/0021-8693(75)90064-2
Oscar Zariski, On the Topology of Algebroid Singularities, Amer. J. Math. 54 (1932), no. 3, 453–465. MR 1507926, DOI 10.2307/2370887
Oscar Zariski, Studies in equisingularity. I. Equivalent singularities of plane algebroid curves, Amer. J. Math. 87 (1965), 507–536. MR 177985, DOI 10.2307/2373019
Oscar Zariski, Studies in equisingularity. II. Equisingularity in codimension $1$ (and characteristic zero), Amer. J. Math. 87 (1965), 972–1006. MR 191898, DOI 10.2307/2373257
Oscar Zariski, Studies in equisingularity. III. Saturation of local rings and equisingularity, Amer. J. Math. 90 (1968), 961–1023. MR 237493, DOI 10.2307/2373492
Oscar Zariski, Characterization of plane algebroid curves whose module of differentials has maximum torsion, Proc. Nat. Acad. Sci. U.S.A. 56 (1966), 781–786. MR 202716, DOI 10.1073/pnas.56.3.781
- 1.
- K. Brauner, Zur Geometrie der Funktionen zweier complexen Veränderlichen, III, IV, Abh. Math. Sem. Hamburg 6 (1928), 8-54.
- 2.
- W. Burau, Kennzeichnung der Schlauchhnoten, Abh. Math. Sem. Hamburg 9 (1932), 125-133. MR 0166066
- 3.
- C. Delorme, Sur la dimension d'un espace de singularité, C. R. Acad. Sci. Paris 280 (1975), 1287-89. MR 437544
- 4.
- D. Eisenbud and W. Neumann, Three-dimensional link theory and invariants of plane curve singularities, Ann. of Math. Studies, No. 110, Princeton, 1985. MR 817982
- 5.
- F. Enriques and O. Chisini, Lezioni sulla theorie geometrica delle equazioni e delle funzioni algebriche, 3 vols., Bologna, 1915, 1918, and 1925.
- 6.
- E. Hecke, Lectures on the theory of algebraic numbers, Graduate Texts in Math., vol. 77, Springer-Verlag, Berlin and New York, 1981. MR 638719
- 7.
- M. Lejeune and B. Teissier, Clôture integrale des ideaux et équisingularité, Sém. École Polytechnique, (1973-1974).
- 8.
- J. Milnor, Singular points of complex hypersurfaces, Ann. of Math. Studies, No. 61, Princeton, 1968. MR 239612
- 9.
- H. C. Pinkham, Deformations of algebraic varieties with G, Astérisque 20 (1974).
- 10.
- J. G. Semple and G. T. Kneebone, Algebraic curves, Oxford, 1959. MR 124801
- 11.
- S. Washburn, Analytically trivial families of local rings, J. Algebra 35 (1975), 528-533. MR 371890
- 12.
- O. Zariski, On the topology of algebroid singularities, Amer. J. Math. 54 (1932), 453-465. MR 1507926
- 13.
- O. Zariski, Studies in equisingularity. I. Equivalent singularities of plane algebroid curves, Amer. J. Math. 87 (1965), 507-536. MR 177985
- 14.
- O. Zariski, Studies in equisingularity. II. Equisingularity in codimension 1 (and characteristic zero), Amer. J. Math. 87 (1965), 972-1006. MR 191898
- 15.
- O. Zariski, Studies in equisingularity. III. Saturation of local rings and equisingularity, Amer. J. Math. 90 (1968), 961-1023. MR 237493
- 16.
- O. Zariski, Characterization of plane algebroid curves whose module of differentials has maximum torsion, Proc. Nat. Acad. Sci. U.S.A. 56 (1966), 781-786. MR 202716
Review Information:
Reviewer:
Sherwood Washburn
Journal:
Bull. Amer. Math. Soc.
18 (1988), 209-214
DOI:
https://doi.org/10.1090/S0273-0979-1988-15651-0