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.

On Clifford's theorem for singular curves

FRANCIOSI, MARCO;
2014

Abstract

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.
Franciosi, Marco; E., Tenni
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/215126
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