Annali dell’Università di Ferrara

, Volume 50, Issue 1, pp 151–165 | Cite as

A result on resolutions of Veronese embeddings

  • Elena Rubei


This paper deals with syzygies of the ideals of the Veronese embeddings. By Green’s Theorem we know thatO P n (d) satisfies Green-Lazarsfeld’s PropertyN pd≥p, ∀n. By Ottaviani-Paoletti’s theorem ifn≥2, d≥3 and 3d−2≤p thenO P n (d) does not satisfy PropertyN p. The casesn≥3, d≥3, d<p<3d−2 are still open (exceptn=d=3). Here we deal with one of these cases, namely we prove thatO P n (3) satisfies PropertyN 4n. Besides we prove thatO P n (d) satisfiesN pn≥p iffO P n (d) satisfiesN p.

Key words

syzyzgies Veronese embedding 

2000 Mathematical Subject Classification

14M25 13D02 


L’argomento di questo articolo sono le sizigie degli ideali delle varietà di Veronese. Per il teorema di Green sappiamo cheO P n (d) soddisfa la proprietàN p di Green-Lazarsfeld ∀d≥p, ∀n. Per il teorema di Ottaviani-Paoletti sen≥2, d≥3 and 3d−2≤p alloraO P n (d) non soddisfa la ProprietàN p. I casin≥3, d≥3, d<p<3d−2 sono ancora aperti (eccetton=d=3). Qui consideriamo uno di tali casi, precisamente proviamo cheO P n (3) soddisfa la ProprietàN 4n. Inoltre proviamo cheO P n (d) soddisfaN pn≥p se e solo seO P p (d) satisfiesN p.


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Copyright information

© Università degli Studi di Ferrara 2004

Authors and Affiliations

  • Elena Rubei
    • 1
  1. 1.Dipartimento di Matematica “U. Dini»FirenzeItalia

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