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The generic Green–Lazarsfeld Secant Conjecture

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Abstract

Using lattice theory on special \(K3\) surfaces, calculations on moduli stacks of pointed curves and Voisin’s proof of Green’s Conjecture on syzygies of canonical curves, we prove the Prym–Green Conjecture on the naturality of the resolution of a general Prym-canonical curve of odd genus, as well as (many cases of) the Green–Lazarsfeld Secant Conjecture on syzygies of non-special line bundles on general curves.

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Acknowledgments

We are grateful to M. Aprodu, D. Eisenbud, J. Harris, R. Lazarsfeld, F.-O. Schreyer, and especially to C. Voisin for many useful discussions related to this circle of ideas.

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Authors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Gavril Farkas & Michael Kemeny

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  1. Gavril Farkas
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  2. Michael Kemeny
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Correspondence to Gavril Farkas.

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Farkas, G., Kemeny, M. The generic Green–Lazarsfeld Secant Conjecture. Invent. math. 203, 265–301 (2016). https://doi.org/10.1007/s00222-015-0595-7

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  • DOI: https://doi.org/10.1007/s00222-015-0595-7

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