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The Green-Lazarsfeld Secant Conjecture is a generalization of Green'sConjecture on syzygies of canonical curves to the cases of arbitrary linebundles. We establish the Green-Lazarsfeld Secant Conjecture for curves ofgenus g in all the divisorial case, that is, when the line bundles that fail tobe (p+1)-very ample form a divisor in the Jacobian of the curve.

Difference varieties and the Green-Lazarsfeld Secant Conjecture