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arXiv · 1105.2253

On Clifford's theorem for singular curves

Marco Franciosi·Elisa Tenni
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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 H^0(C, I_S K_C) contains a generically invertible section). Under some general assumptions on S or C we show that h^0(C, I_S K_C) <= p_a(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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Marco Franciosi, Elisa Tenni. 2013-04-05. On Clifford's theorem for singular curves. https://doi.org/10.1112/plms%2Fpdt019

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