Topological types and multiplicities of isolated quasi-homogeneous surface singularities
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- by Stephen S.-T. Yau PDF
- Bull. Amer. Math. Soc. 19 (1988), 447-454
References
- V. I. Arnol′d, Normal forms of functions in the neighborhood of degenerate critical points, Uspehi Mat. Nauk 29 (1974), no. 2(176), 11–49 (Russian). Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiĭ (1901–1973), I. MR 0516034
- Norbert A’Campo, La fonction zêta d’une monodromie, Comment. Math. Helv. 50 (1975), 233–248 (French). MR 371889, DOI 10.1007/BF02565748 2. K. Brauner, Zur Geometrie der Funktionen Zweier komplexen Veränderlicken, Abh. Math. Sem. Hamburg 6 (1928), 1-54. 3. W. Burau, Kennzeichnung der Schlauchknoten, Abh. Math. Sem. Hamburg 9 (1932), 125-133.
- Gert-Martin Greuel, Constant Milnor number implies constant multiplicity for quasihomogeneous singularities, Manuscripta Math. 56 (1986), no. 2, 159–166. MR 850367, DOI 10.1007/BF01172153
- Henry B. Laufer, Tangent cones for deformations of two-dimensional quasi-homogeneous singularities, Singularities (Iowa City, IA, 1986) Contemp. Math., vol. 90, Amer. Math. Soc., Providence, RI, 1989, pp. 183–197. MR 1000602, DOI 10.1090/conm/090/1000602
- Lê Dũng Tráng, Topologie des singularités des hypersurfaces complexes, Singularités à Cargèse (Rencontre Singularités Géom. Anal., Inst. Études Sci., Cargèse, 1972) Astérisque, Nos. 7 et 8, Soc. Math. France, Paris, 1973, pp. 171–182 (French). MR 0361147
- Lê Dũng Tráng, Three lectures on local monodromy, Lecture Notes Series, No. 43, Aarhus Universitet, Matematisk Institut, Aarhus, 1974. Lectures 1974. MR 0372242
- Lê Dũng Tráng and B. Teissier, Report on the problem session, Singularities, Part 2 (Arcata, Calif., 1981) Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, R.I., 1983, pp. 105–116. MR 713239 9. M. Lejeune, Sur l’equivalence des singularités des courbes algebroides planes, Coefficients de Newton, Centre de Math, de l’École Polytechnique, 1969.
- 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
- John Milnor and Peter Orlik, Isolated singularities defined by weighted homogeneous polynomials, Topology 9 (1970), 385–393. MR 293680, DOI 10.1016/0040-9383(70)90061-3
- Walter D. Neumann, A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves, Trans. Amer. Math. Soc. 268 (1981), no. 2, 299–344. MR 632532, DOI 10.1090/S0002-9947-1981-0632532-8
- Peter Orlik and Philip Wagreich, Isolated singularities of algebraic surfaces with C$^{\ast }$ action, Ann. of Math. (2) 93 (1971), 205–228. MR 284435, DOI 10.2307/1970772
- Donal B. O’Shea, Topologically trivial deformations of isolated quasihomogeneous hypersurface singularities are equimultiple, Proc. Amer. Math. Soc. 101 (1987), no. 2, 260–262. MR 902538, DOI 10.1090/S0002-9939-1987-0902538-0
- B. Perron, Conjugaison topologique des germes de fonctions holomorphes à singularité isolée en dimension trois, Invent. Math. 82 (1985), no. 1, 27–35 (French). MR 808107, DOI 10.1007/BF01394777
- J. E. Reeve, A summary of results in the topological classification of plane algebroid singularities, Univ. e Politec. Torino Rend. Sem. Mat. 14 (1954/55), 159–187. MR 96663
- A. N. Varchenko, Zeta-function of monodromy and Newton’s diagram, Invent. Math. 37 (1976), no. 3, 253–262. MR 424806, DOI 10.1007/BF01390323
- Etsuo Yoshinaga, Topological types of isolated singularities defined by weighted homogeneous polynomials, J. Math. Soc. Japan 35 (1983), no. 3, 431–436. MR 702767, DOI 10.2969/jmsj/03530431
- 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, Some open questions in the theory of singularities, Bull. Amer. Math. Soc. 77 (1971), 481–491. MR 277533, DOI 10.1090/S0002-9904-1971-12729-5
- Oscar Zariski, General theory of saturation and of saturated local rings. II. Saturated local rings of dimension $1$, Amer. J. Math. 93 (1971), 872–964. MR 299607, DOI 10.2307/2373741
Additional Information
- Journal: Bull. Amer. Math. Soc. 19 (1988), 447-454
- MSC (1985): Primary 32B99; Secondary 32C40
- DOI: https://doi.org/10.1090/S0273-0979-1988-15695-9
- MathSciNet review: 935021