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Martens' dimension theorem for curves of even gonality
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Abstract
For a smooth projective irreducible algebraic curve C of oddgonality, the maximal possible dimension of the variety ofspecial linear systems W^r_d(C) is d-3r by a result of M.Coppens et al. cite{CKM}. This bound also holds if C does notadmit an involution. Furthermore it is known that if dimW^r_d(C)ge d-3r-1 for a curve C of odd gonality, then C isof very special type of curves by a recent progress made by G.Martens cite{Ma} and Kato-Keem cite{KK}. The purpose of thispaper is to pursue similar results for curves of even gonalitywhich does not admit an involution.
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