Abstract
Let C be a smooth projective algebraic curve which is not a curve of even gonality admitting an automorphism of order 2. Under this rather mild restriction on C, we establish a stronger dimension theoretic statement concerning the variety of special linear systems; we prove that if dim W d r(C)⩾d−3r−2⩾0 for some d, r>0 with d⩽ g−5 and g⩾21, then C is a k-gonal curve with k⩽6, a 4-sheeted covering of an elliptic curve or a plane curve of degree 8.
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