New findings demonstrate high degree embeddings meet Green's Np conditions in curves, suggesting broader implications for syzygies.
We develop analogues of Green’s Nₚ conditions for subvarieties of weighted projective space, and we prove that such Nₚ conditions are satisfied for high degree embeddings of curves in weighted projective space. A key technical result links positivity with low degree (virtual) syzygies in wide generality, including cases where normal generation fails.
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Brown et al. (2025) studied this question.