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