Syzygy conjecture for general projections of paracanonical curves

Assume that CC is a generic paracanonical curve of genus g11g\geq 11, embedded by the paracanonical bundle ωCη\omega_C\otimes\eta, where η\eta is a generic non-trivial torsion line bundle. Let pH0(ωCη)p\in H^0(\omega_C\otimes\eta)^\vee be a generic point, and let CC' be the projection of CC away from pp. Then the paracanonical projection conjecture. The Betti diagram of CC' satisfies N~Cliff(C)4\widetilde{N}_{\operatorname{Cliff}(C)-4}, and the length of its linear strands is Cliff(C)3\operatorname{Cliff}(C)-3. This predicts the syzygies of general projections of paracanonical curves in genus at least 1111; the statement is presented as a conjecture and no resolution is given in the source.

Sources & referencesView supporting material

Primary source

Li Li, “Syzygies of general projections of canonical and paracanonical curves”, arXiv:2407.08492 (2024).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.