Pacific Journal of Mathematics

On Gorenstein surface singularities with fundamental genus $p_f\geq 2$ which satisfy some minimality conditions.

Tadashi Tomaru

Article information

Source
Pacific J. Math., Volume 170, Number 1 (1995), 271-295.

Dates
First available in Project Euclid: 6 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102371117

Mathematical Reviews number (MathSciNet)
MR1359980

Zentralblatt MATH identifier
0848.14017

Subjects
Primary: 14J17: Singularities [See also 14B05, 14E15]
Secondary: 14E15: Global theory and resolution of singularities [See also 14B05, 32S20, 32S45]

Citation

Tomaru, Tadashi. On Gorenstein surface singularities with fundamental genus $p_f\geq 2$ which satisfy some minimality conditions. Pacific J. Math. 170 (1995), no. 1, 271--295. https://projecteuclid.org/euclid.pjm/1102371117


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References

  • [1] M. Artin, On isolatedrational singularities of surfaces,Amer. J. Math., 88 (1963), 129-138.
  • [2] E. Brieskorn, Rational Singularitdten komplexer Fldchen, Inve. Math., 4 (1969), 336-358.
  • [3] M. Demazure, Anneaux gradues normaux, in Seminaire Demazure-Giraud-Teissier, Singularites des surfaces, Ecole Polytechnique (1979).
  • [4] I.V. Dolgachev, Weighted projected varities. GroupActions and Vector Fields (Proc. Polish-North Ameri. Sem., Vancouver (1981)), Lecture Notes in Math.,956, Springer- Verlag (1982), 34-71.
  • [5] F. Hidaka and K-i. Watanabe, Normal Gorenstein surfaces with amplecanonical divisor,Tokyo J. Math., 4 (1989), 319-330.
  • [6] H. Laufer, On rational singularities,Amer. J. Math., 94 (1972), 597-608.
  • [7] H. Laufer, On minimally elliptic singularities, Amer. J. Math., 99, No. 6 (1977), 1257-1295.
  • [8] M. Oka, On the Resolution of the HypersurfaceSingularities, Adv. Stud, in Pure Math., 8 (1986), 405-436.
  • [9] P. Orlik and P. Wagreich, Isolatedsingularities of algebraic surface with C*-action, Ann. of Math., 93 (1971), 205-228.
  • [10] H. Pinkham, Normal surface singularities with C*-action, Math. Ann., 227 (1977), 183-193.
  • [11] M. Reid, Elliptic Gorenstein singularities of surfaces,Preprint, 1978.
  • [12] O. Riemenschneider, Deformationen von Quotientensingularitten (nach zyklischen Gruppen),Math. Ann., 209 (1974), 211-248.
  • [13] J. Stevens, KulikovSingularities,Thesis, 1985.
  • [14] M.Tomari, Maximal-Ideal-Adic Filtration onR*Oy for NormalTwo-Dimensional Singularities,Adv. Stud, in Pure Math., 8 (1986),633-647.
  • [15] M. Tomari and K-i. Watanabe, Filtered Rings, Filtered Blowing-Ups andNor- mal Two-Dimensional Singularitieswith "Star-Shaped" Resolution, Publ. Res.Inst. Math. Soc,Kyoto Univ., 25 (1989),681-740.
  • [16] T. Tomaru, Cyclic quotients of 2-dimensionalquasi-homogeneous hypersurface sin- gularities,Math. Z.,210 (1992),225-244.
  • [17] T. Tomaru, Onnumerically Gorenstein quasi-simple ellipticsingularitieswithC* -action, Proc. Amer. Math. Soc, 120 (1994), 67-71.
  • [18] P. Wagreich,Elliptic singulrities of surfaces,Amer. J. Math., 92 (1970),421-454.
  • [19] K-i.Watanabe, Some remarksconcerning Demazure's constructionof normal graded rings,Nagoya Math. J., 83 (1981), 203-211.
  • [20] Ki. Watanabe, On plurigenera of normal isolatedsingularities I, Math. Ann.,250 (1980), 65-94.
  • [21] Ki. Watanabe, On plurigenera of normal isolated singularities II, Adv. Stud, in Pure Math., 8 (1986), 671-685.
  • [22] S.S.-T. Yau, Normal two-dimensionalelliptic singularities, Trans. Amer. Math. Soc, 254 (1979),117-134.
  • [23] S.S.-T. Yau, On strongly elliptic singularities,Amer. J. Math., 101 (1979),855-884.
  • [24] S.S.-T. Yau, On maximally elliptic singularities, Trans. Amer. Math. Soc (2), 257 (1980),269-329.
  • [25] E. Yoshinagaand S. Ohyanagi, A criterion for 2-dimensionalnormalsingularities to weaklyelliptic,Sci.Rep.Yokohama National Univ. Sec 2, 26 (1979), 5-7.