On Clifford's theorem for singular curves
Abstract
Let C be a 2-connected Gorenstein curve either reduced or contained in a smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim scheme such that the space H0(C, IS KC) contains a generically invertible section). Under some general assumptions on S or C we show that h0(C, IS KC) <= pa(C) - deg (S)/2 and if equality holds then either S is trivial, or C is honestly hyperelliptic or 3-disconnected. As a corollary we give a generalization of Clifford's theorem for reduced curves.
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