MARTENS` DIMENSION THEOREM FOR CURVES OF EVEN GONALITY Kato, Takao;
For a smooth projective irreducible algebraic curve C of odd gonality, the maximal possible dimension of the variety of special linear systems (C) is d－3r by a result of M. Coppens et at. . This bound also holds if C does not admit an involution. Furthermore it is known that if dim 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  and Kato-Keem . The purpose of this paper is to pursue similar results for curves of even gonality which does not admit an involution.