On syzygies of Segre embeddings

Rubei, Elena

doi:10.1090/S0002-9939-02-06597-8

On syzygies of Segre embeddings
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by Elena Rubei PDF

Proc. Amer. Math. Soc. 130 (2002), 3483-3493 Request permission

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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