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MARTENS' DIMENSION THEOREM FOR CURVES OF EVEN GONALITY

  • Kato, Takao
  • Published : 2002.09.01

Abstract

For a smooth projective irreducible algebraic curve C of odd gonality, the maximal possible dimension of the variety of special linear systems ${W^r}_d$(C) is d-3r by a result of M. Coppens et at. [4]. This bound also holds if C does not admit an involution. Furthermore it is known that if dim ${W^r}_d(C)qeq$ d-3r-1 for a curve C of odd gonality, then C is of very special type of curves by a recent progress made by G. Martens [11] and Kato-Keem [9]. The purpose of this paper is to pursue similar results for curves of even gonality which does not admit an involution.

Keywords

algebraic curves;linear series;gonality;Brill-Noether theory

References

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  11. Geometry of Algebraic Curves Ⅰ E. Arbarello;M. Cornalba;P. A. Griffiths;J. Harris
  12. Curves in projective space, Seminaire de mathematiques superieures J. Harris
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Cited by

  1. On the variety Wdr(C) whose dimension is at least d−3r−2 vol.192, pp.1-3, 2004, https://doi.org/10.1016/j.jpaa.2004.01.006