Syzygies of Veronese Embeddings

2001/01/01 by Giorgio Ottaviani, Raffaella Paoletti · 10 citations
Mathematics · Biochemistry, Genetics and Molecular Biology · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Biological Activity of Diterpenoids and Biflavonoids

paper · pdf · doi:10.1023/a:1002662809474

Abstract

We prove that the Veronese embedding φ _{\cal O \Bbb P} n (d): \Bbb P n \hookrightarrow \Bbb P N with n [ges ]2, d [ges ]3 does not satisfy property N p (according to Green and Lazarsfeld) if p [ges ]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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• A result on resolutions of Veronese embeddings
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• On Higher Syzygies of ruled varieties over a curve
• Asymptotic Np property of rational surfaces
• Some effects of Veronese map on syzygies of projective varieties
• Noncomplete embeddings of rational surfaces
• Asymptotic Syzygies in the Setting of Semi-Ample Growth
• Generation and syzygies of the first secant variety

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