Abstract
We prove that the Veronese embedding ϕ Oℙ n(d):ℙn↪ ℙN with n≥2, d≥3 does not satisfy property N p (according to Green and Lazarsfeld) if p≥3d−2. We make the conjecture that also the converse holds. This is true for n=2 and for n=d=3.
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Ottaviani, G., Paoletti, R. Syzygies of Veronese Embeddings. Compositio Mathematica 125, 31–37 (2001). https://doi.org/10.1023/A:1002662809474
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DOI: https://doi.org/10.1023/A:1002662809474