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On syzygies of Segre embeddings

Author: Elena Rubei
Journal: Proc. Amer. Math. Soc. 130 (2002), 3483-3493
MSC (2000): Primary 14M25, 13D02
Published electronically: May 9, 2002
MathSciNet review: 1918824
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Abstract: We study the syzygies of the ideals of the Segre embeddings. Let $d \in {\mathbf N}$, $ d \geq 3$; we prove that the line bundle ${\mathcal O}(1,...,1)$on the $P^1 \times ... \times P^1 $ ($d$ copies) satisfies Property $N_p$ of Green-Lazarsfeld if and only if $p \leq 3$. Besides we prove that if we have a projective variety not satisfying Property $N_p$ for some $p$, then the product of it with any other projective variety does not satisfy Property $N_p$. From this we also deduce other corollaries about syzygies of Segre embeddings.

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Additional Information

Elena Rubei
Affiliation: Dipartimento di Matematica “U. Dini”, via Morgagni 67/A, 50134 Firenze, Italia

Received by editor(s): December 20, 2000
Received by editor(s) in revised form: July 13, 2001
Published electronically: May 9, 2002
Communicated by: Michael Stillman
Article copyright: © Copyright 2002 American Mathematical Society