Tokyo Journal of Mathematics

Classification of Sextics of Torus Type

Mutsuo OKA and Duc Tai Pho

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Abstract

In [7], the second author classified configurations of the singularities on tame sextics of torus type. In this paper, we give a complete classification of the singularities on irreducible sextic of torus type, without assuming the tameness of the sextics. We show that there exist 121 configurations and there are 5 pairs and a triple of configurations for which the corresponding moduli spaces coincide, ignoring the respective torus decomposition.

Article information

Source
Tokyo J. Math., Volume 25, Number 2 (2002), 399-433.

Dates
First available in Project Euclid: 5 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1244208862

Digital Object Identifier
doi:10.3836/tjm/1244208862

Mathematical Reviews number (MathSciNet)
MR1948673

Zentralblatt MATH identifier
1062.14036

Subjects
Primary: 14H10: Families, moduli (algebraic)
Secondary: 14H45: Special curves and curves of low genus 32S05: Local singularities [See also 14J17]

Citation

OKA, Mutsuo; Pho, Duc Tai. Classification of Sextics of Torus Type. Tokyo J. Math. 25 (2002), no. 2, 399--433. doi:10.3836/tjm/1244208862. https://projecteuclid.org/euclid.tjm/1244208862


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References

  • E. Horikawa, On deformations of quintic surfaces. Invent. Math., 31 (1975), 43–85.
  • J. Milnor, Singular Points of Complex Hypersurface, Annals Math. Studies 61 (1968), Princeton Univ. Press.
  • M. Namba, Geometry of Projective Algebraic Curves, Decker (1984).
  • M. Oka, Geometry of reduced sextics of torus type, preprint in, preparation.
  • M. Oka, Geometry of cuspidal sextics and their dual curves, Singularities–-Sapporo 1998, Kinokuniya (2000), 245–277.
  • M. Oka and D. T. Pho, Fundamental group of sextic of torus type, Trends in Singularities, Birkhäuser (2002), 151–180.
  • D. T. Pho, Classification of singularities on torus curves of type $(2,3)$, Kodai Math. J., 24 (2) (2000), 259–284.
  • T. Shioda and H. Inose, On singular $K3$ surfaces, Complex analysis and algebraic geometry, Iwanami Shoten (1977), 119–136.
  • H.-o. Tokunaga, (2,3) torus sextics and the Albanese images of 6-fold cyclic multiple planes, Kodai Math. J., 22 (2) (1999), 222–242.
  • J.-G. Yang, Sextic curves with simple singularities, Tohoku Math. J., 48 (2) (1996), 203–227.