Annali di Matematica Pura ed Applicata (1923 -)

, Volume 198, Issue 6, pp 2167–2181 | Cite as

Clifford index for reduced curves

  • Marco FranciosiEmail author


We extend the notion of Clifford index to reduced curves with planar singularities by considering rank 1 torsion-free sheaves. We investigate the behaviour of the Clifford index with respect to the combinatorial properties of the curve, and we show that Green’s conjecture holds for certain classes of curves given by the union of two irreducible components.


Algebraic curve Clifford index Green’s conjecture 

Mathematics Subject Classification

14H20 14C20 14H51 



The author is grateful for support by the PRIN project 2015EYPTSB\(\_\)010 “Geometry of Algebraic Varieties” of Italian MIUR. The author would like to thank Elisa Tenni for deep and stimulating discussions on these arguments and the anonymous referee for his/her interesting observations.


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© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly

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