Proceedings of the Japan Academy, Series A, Mathematical Sciences

Canonical curves of genus eight

Manabu Ide and Shigeru Mukai

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A non-tetragonal curve of genus 8 is a complete intersection of divisors in either $\mathbf{P}^2 \times \mathbf{P}^2$, a 6-dimensional weighted Grassmannian or the 8-dimensional Grassmannian.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 79, Number 3 (2003), 59-64.

First available in Project Euclid: 18 May 2005

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Zentralblatt MATH identifier

Primary: 14H45: Special curves and curves of low genus

Canonical curve gonality Grassmann variety


Ide, Manabu; Mukai, Shigeru. Canonical curves of genus eight. Proc. Japan Acad. Ser. A Math. Sci. 79 (2003), no. 3, 59--64. doi:10.3792/pjaa.79.59.

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  • Arbarello, E., Cornalba, M., Griffiths, P., and Harris, J.: Geometry of Algebraic Curves Vol. I. Springer-Verlag, New York (1985).
  • Gantmacher, F. A.: The Theory of Matrices Vol. 2. Chelsea, New York (1959).
  • Griffiths, P., and Harris, J.: Principles of Algebraic Geometry. John Wiley & Sons, Inc., New York (1978).
  • Hartshorne, R.: Algebraic Geometry. Springer-Verlag, New York (1977).
  • Ide, M.: Every curves of genus not greater than eight lies on a K3 surface. (2002). (Preprint).
  • Mukai, S.: Curves and symmetric spaces. Proc. Japan Acad., 68A, 7–10 (1992).
  • Mukai, S.: Curves and Grassmannians. Algebraic Geometry and Related Topics, Inchoen, Korea, 1992 (eds. Yang, J.-H. et al.). International Press, Boston, pp. 19–40 (1993).