Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A THEOREM OF CLIFFORD TYPE FOR LINEAR SYSTEMS ON CURVES

  • Published : 2005.02.01
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Abstract

This paper concerns the relation between the degree and the projective dimension of linear systems on curves. We generalize Clifford's theorem and its improvement by Coppens and G. Martens and classify the special curves for our problem, and estimate their gonality.

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References

  1. R. D. M. Accola: On Castelnuovo's inequality for algebraic curves I, Trans. Amer. Math. Soc. 251 (1979), 357-373 https://doi.org/10.2307/1998699
  2. E. Arbarello, M. Cornalba, P. A. Griffiths and J. Harris: Geometry of Algebraic Curves Vol. I, Grundlehren 267, Springer-Verlag, 1985
  3. M. Coppens and T. Kato The gonality of smooth curves with plane models, Manuscripta Math. 70 (1990), 5-25 https://doi.org/10.1007/BF02568358
  4. M. Coppens, C. Keem and G. Martens Primitive linear series on curves, Manuscripta Math. 77 (1992), 237-264 https://doi.org/10.1007/BF02567056
  5. M. Coppens and G. Martens Secant spaces and Clifford's theorem, Compositio Math. 78 (1991), 193-212
  6. D. Eisenbud and J. Harris Curves in Projective Space, Les presses de l'universite de Montreal, Montreal, 1982
  7. D. Eisenbud, H. Lange, G. Martens and F.-O. Schreyer The Clifford dimension of a projective curve, Compositio Math. 72 (1989), 173-204
  8. R. Hartshorne Algebraic Geometry, Graduate Texts in Math. 52, Springer-Verlag, 1977
  9. G. Martens The gonality of curves on a Hirzebruch surface, Arch. Math. 67 (1996), 349-352 https://doi.org/10.1007/BF01197600
  10. M. Ohkouchi and F. Sakai The gonality of singular plane curves, Algebraic Ge- ometry and Related Topics, Proceeding of the Korea-Japan Joint Workshop in Mathematics 2002, Yamaguchi University, 2003