Tohoku Mathematical Journal

Normal two-dimensional hypersurface triple points and the Horikawa type resolution

Tadashi Ashikaga

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 44, Number 2 (1992), 177-200.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178227335

Digital Object Identifier
doi:10.2748/tmj/1178227335

Mathematical Reviews number (MathSciNet)
MR1161610

Zentralblatt MATH identifier
0801.14011

Subjects
Primary: 14J17: Singularities [See also 14B05, 14E15]
Secondary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 32S10: Invariants of analytic local rings 32S25: Surface and hypersurface singularities [See also 14J17] 32S55: Milnor fibration; relations with knot theory [See also 57M25, 57Q45]

Citation

Ashikaga, Tadashi. Normal two-dimensional hypersurface triple points and the Horikawa type resolution. Tohoku Math. J. (2) 44 (1992), no. 2, 177--200. doi:10.2748/tmj/1178227335. https://projecteuclid.org/euclid.tmj/1178227335


Export citation

References

  • [AK] T. ASHIKAGA AND K. KONNO, Examples of degenerations of Castelnuovo surfaces, J. Math. Soc. Japan 43 (1991), 229-246.
  • [D] A. DURFEE, The signature of smoothings of complex surface singularities, Math. Ann. 232 (1978), 85-98.
  • [FN] A. FUJIKI AND S. NAKANO, Supplement to "On the inverse of monoidal transformation", Publ Res. Inst. Math. Sci., Kyoto Univ. 7 (1972), 637-644.
  • [FMS] S. FUKUHARA, Y. MATUMOTO AND K. SAKAMOTO, Casson's invariant of Seifert homology 3-sphere, Math. Ann. 287 (1990) 275-285.
  • [HI] E. HORIKAWA, On deformations of quintic surfaces, Invent. Math. 31 (1975), 43-85
  • [H2] E. HORIKAWA, On algebraic surfaces with pencils of curves of genus two, in Complex Analysis an Algebraic Geometry (W. L. Baily, Jr. and T. Shioda eds.), pp. 79-90, a volume dedicated to K. Kodaira, Iwanami Shoten and Cambridge Univ. Press, Tokyo and Cambridge, 1977.
  • [H3] E. HORIKAWA, Algebraic surfaces of general type with small c2v V. J. Fac. Sci. Univ. Tokyo 2 (1981), 745-755.
  • [L] H. LAUFER, On for surface singularities, in Several Complex Variables, pp. 45-49, Proc. Symposi in Pure Math. 30, Providence, R. I., Amer. Math. Soc, 1977.
  • [Mil] J. MILNOR, Singular Points of Complex Hypersurfaces, Ann. of Math. Studies 61 (1968), Princeto Univ. Press.
  • [Mir] R. MIRANDA, Triple covers in algebraic geometry, Amer. J. Math. 107 (1985), 1123-1158
  • [NW] W. NEUMANN AND J. WAHL, Casson invariant of links of singularities, Comment. Math. Helvetic 65 (1990), 58-78.
  • [P] U. PERSSON, On Chern invariants of surfaces of general type, Compositio Math. 43 (1981), 3-58
  • [SI] K. SAITO, Einfach-elliptische Singularitaten, Invent. Math. 23 (1974), 289-325
  • [S2] K. SAITO, The zeroes of characteristic function f for the exponents of a hypersurface isolate singular points, in Algebraic varieties and Analytic varieties (S. Iitaka ed.), pp. 195-217, Advanced Studies in Pure Math. 1, Kinokuniya and North Holland, Tokyo and Amsterdam, 1983.
  • [Tl] M. TOMARI, A geometric characterization of normal two-dimensional singularities of multiplicit two with/?fll, Publ. Res. Inst. Math. Sci., Kyoto Univ. 20 (1984), 1-20.
  • [T2] M. TOMARI, The inequality 8/?3 for hypersurface two-dimensional isolated double points, preprint.
  • [W] J. WAHL, Smoothings of normal surface singularities, Topology 20 (1981), 219-246
  • [XY1] Y. Xu AND S. S. T. YAU, The inequality \2pg – 4 for hypersurface weakly elliptic singularities, in Singularities 1986, Iowa (R. Randell, ed.), pp. 317-344, Contemporary Math. 90, Amer. Math. Soc, 1989.
  • [XY2] Y. Xu AND S. S. T. YAU, Durfee conjecture and coordinate free characterization of homogeneou singularities, preprint.