Osaka Journal of Mathematics

The gonality conjecture for curves on certain toric surfaces

Ryo Kawaguchi

Full-text: Open access

Abstract

The gonality is one of important invariants in the study of linear systems on curves. The gonality conjecture which was posed by Green and Lazarsfeld predicts that we can read off the gonality of a curve from any one line bundle of sufficiently large degree on the curve. This conjecture had been proved for curves on Hirzebruch surfaces by Aprodu. In this artlcle, we will extend this result for curves on certain toric surfaces.

Article information

Source
Osaka J. Math., Volume 45, Number 1 (2008), 113-126.

Dates
First available in Project Euclid: 14 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1205503560

Mathematical Reviews number (MathSciNet)
MR2416652

Zentralblatt MATH identifier
1133.14306

Subjects
Primary: 14H51: Special divisors (gonality, Brill-Noether theory)
Secondary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]

Citation

Kawaguchi, Ryo. The gonality conjecture for curves on certain toric surfaces. Osaka J. Math. 45 (2008), no. 1, 113--126. https://projecteuclid.org/euclid.ojm/1205503560


Export citation

References

  • M. Aprodu: On the vanishing of higher syzygies of curves, Math. Z. 241 (2002), 1--15.
  • M. Green and R. Lazarsfeld: The nonvanishing of certain Koszul cohomology groups, J. Differential Geom. 19 (1984), 168--170, (Appendix to [4]).
  • M. Green and R. Lazarsfeld: On the projective normality of complete linear series on an algebraic curve, Invent. Math. 83 (1985), 73--90.
  • M.L. Green: Koszul cohomology and the geometry of projective varieties, J. Differential Geom. 19 (1984), 125--171.
  • G. Martens: The gonality of curves on a Hirzebruch surface, Arch. Math. (Basel) 67 (1996), 349--352.
  • M. Mustaţă: Vanishing theorems on toric varieties, Tohoku Math. J. (2) 54 (2002), 451--470.
  • T. Oda: Convex Bodies and Algebraic Geometry, Springer-Verlag, Berlin, 1988.