MARTENS' DIMENSION THEOREM FOR CURVES OF EVEN GONALITY

Title & Authors
MARTENS' DIMENSION THEOREM FOR CURVES OF EVEN GONALITY
Kato, Takao;

Abstract
For a smooth projective irreducible algebraic curve C of odd gonality, the maximal possible dimension of the variety of special linear systems $\small{{W^r}_d}$(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 $\small{{W^r}_d(C)qeq}$ 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;
Language
English
Cited by
1.
On the variety Wdr(C) whose dimension is at least d−3r−2, Journal of Pure and Applied Algebra, 2004, 192, 1-3, 159
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