Problem dossier · Algebra
Green's conjecture on syzygies
For a smooth canonical curve, the vanishing pattern of the syzygies of its canonical embedding is governed exactly by its Clifford index.
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Status
Proved for generic curves (Voisin 2002–05) and various classes; open in full generality for arbitrary smooth curves.
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The Angle of Attack
Compute syzygy tables (Macaulay2) for low-genus curves across special gonality strata; hunt for the boundary cases where genericity assumptions bite.
Tags: syzygies · canonical curves · clifford index · computational algebraic geometry
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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