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arXiv · 0811.2407

Regularity of smooth curves in biprojective spaces

Victor Lozovanu
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Abstract

Maclagan and Smith \cite{MaclaganSmith} developed a multigraded version of Castelnuovo-Mumford regularity. Based on their definition we will prove in this paper that for a smooth curve $C\subseteq ¶^a\times¶^b$ $(a, b\geq 2)$ of bidegree $(d_1,d_2)$ with nondegenerate birational projections the ideal sheaf $\mathcal{I}_{C|¶^a\times¶^b}$ is $(d_2-b+1,d_1-a+1)$-regular. We also give an example showing that in some cases this bound is the best possible.

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Victor Lozovanu. 2008-11-14. Regularity of smooth curves in biprojective spaces. https://arxiv.org/abs/0811.2407

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