On Clifford's theorem for singular curves

Let C be a 2‐connected projective curve either reduced with planar singularities or contained in a smooth algebraic surface and let S be a subcanonical cluster (that is, a zero‐dimensional scheme such that the space H0(C, ℐS KC) contains a generically invertible section). Under some general assumpti...

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Bibliographic Details
Published in:Proceedings of the London Mathematical Society 2014-01, Vol.108 (1), p.225-252
Main Authors: Franciosi, Marco, Tenni, Elisa
Format: Article
Language:English
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Summary:Let C be a 2‐connected projective curve either reduced with planar singularities or contained in a smooth algebraic surface and let S be a subcanonical cluster (that is, a zero‐dimensional 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)−½ deg (S) 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 with planar singularities.
ISSN:0024-6115
1460-244X
DOI:10.1112/plms/pdt019