• 대한수학회지
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• 제37권3호
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• pp.359-369
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• 2000

Let X be an integral Gorenstein projective curve with g:=pa(X) $\geq$ 3. Call $G^r_d$ (X,**) the set of all pairs (L,V) with L$\epsilon$Pic(X), deg(L) = d, V $\subseteq$ H^0$(X,L), dim(V) =r+1 and V spanning L. Assume the existence of integers d, r with 1 $\leq$ r$\leq$ d $\leq$ g-1 such that there exists an irreducible component, , of $G^r_d$(X,**) with dim($\Gamma$) $\geq$ d - 2r and such that the general L$\geq$$\Gamma$ is spanned at every point of Sing(X). Here we prove that dim( ) = d-2r and X is hyperelliptic.

• 대한수학회지
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• 제39권5호
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• pp.665-680
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• 2002

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.