Asymptotic Syzygies of Weighted Projective Spaces

By adapting methods of Ein-Erman-Lazarsfeld, we prove an analogue of the Ein-Lazarsfeld result on asymptotic syzygies for Veronese embeddings, in the setting of weighted projective spaces of the form $\mathbb{P}(1^n,2)$.

💡 Research Summary

The paper investigates the asymptotic behavior of syzygies for weighted projective spaces of the form 𝙿(1ⁿ, 2) under Veronese embeddings. The author adapts the monomial technique introduced by Ein‑Erman‑Lazarsfeld (the “EEL method”) to the non‑standard graded setting that arises when one of the variables has weight 2. The classical EEL method works for the standard graded polynomial ring k