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Syzygies of Veronese Embeddings

Published online by Cambridge University Press:  04 December 2007

Giorgio Ottaviani  and
Raffaella Paoletti
Giorgio Ottaviani
Affiliation:
Dipartimento di Matematica ‘U. Dini’, Università di Firenze, viale Morgagni 67/A, I 50134 Firenze, Italy. E-mail: ottavian@math.unifi.it
Raffaella Paoletti
Affiliation:
Dipartimento di Matematica ed Applicazioni per l'Architettura, Università di Firenze, Piazza Ghiberti 27, I 50122 Firenze, Italy. E-mail: raffy@math.unifi.it
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Abstract

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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 Np (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.

Keywords

Veronese embeddingfree resolutionsyzygy
Type
Research Article
Information
Compositio Mathematica , Volume 125 , Issue 1 , January 2001 , pp. 31 - 37
Copyright
© 2001 Kluwer Academic Publishers