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Inventiones mathematicae

, Volume 203, Issue 1, pp 265–301 | Cite as

The generic Green–Lazarsfeld Secant Conjecture

  • Gavril FarkasEmail author
  • Michael Kemeny
Article

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.

Notes

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany

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