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On Clifford's theorem for singular curves (2014)

Franciosi, M., Tenni, E.

Oxford University Press

In: Proceedings of the London Mathematical Society

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Publication Date: 2014-01-18

Description: 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 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 )–1/2 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.

Print ISSN: 0024-6115

Electronic ISSN: 1460-244X

Topics: Mathematics

Published by Oxford University Press

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