Mathematische Zeitschrift

, Volume 288, Issue 3–4, pp 1157–1164 | Cite as

The canonical syzygy conjecture for ribbons

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Abstract

Green’s canonical syzygy conjecture asserts a simple relationship between the Clifford index of a smooth projective curve and the shape of the minimal free resolution of its homogeneous ideal in the canonical embedding. We prove the analogue of this conjecture formulated by Bayer and Eisenbud for a class of non-reduced curves called ribbons. Our proof uses the results of Voisin and Hirschowitz–Ramanan on Green’s conjecture for general smooth curves.

Keywords

Canonical syzygy conjecture Ribbons Green’s conjecture Koszul cohomology 

Mathematics Subject Classification

14H51 13D02 

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© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Department of MathematicsThe University of GeorgiaAthensUSA

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