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arXiv · 1408.4164

The generic Green-Lazarsfeld secant conjecture

Gavril Farkas·Michael Kemeny
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Abstract

Generalizing the well-known Green Conjecture on syzygies of canonical curves, Green and Lazarsfeld formulated in 1986 the Secant Conjecture predicting that a line bundle L of sufficiently high degree on a curve has a non-linear p-syzygy if and only if L fails to be (p+1)-very ample. Via lattice theory for special K3 surfaces, Voisin's solution of the classical Green Conjecture and calculations on moduli stacks of pointed curves, we prove: (1) The Green-Lazarsfeld Secant Conjecture in various degree of generality, including its strongest possible form in the divisorial case in the universal Jacobian. (2) The Prym-Green Conjecture on the naturality of the resolution of a general Prym-canonical curve of odd genus.

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Gavril Farkas, Michael Kemeny. 2015-03-24. The generic Green-Lazarsfeld secant conjecture. https://doi.org/10.1007/s00222-015-0595-7

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