On syzygies of Segre embeddings
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- by Elena Rubei
- Proc. Amer. Math. Soc. 130 (2002), 3483-3493
- DOI: https://doi.org/10.1090/S0002-9939-02-06597-8
- Published electronically: May 9, 2002
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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.References
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Bibliographic Information
- Elena Rubei
- Affiliation: Dipartimento di Matematica “U. Dini”, via Morgagni 67/A, 50134 Firenze, Italia
- Email: rubei@math.unifi.it
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3483-3493
- MSC (2000): Primary 14M25, 13D02
- DOI: https://doi.org/10.1090/S0002-9939-02-06597-8
- MathSciNet review: 1918824