Maclagan and Smith developed a multigraded version of Castelnuovo-Mumford regularity. Based on their de nition we will prove in this paper that for a smooth curve C inside biprojective space of bidegree (d1,d2) with nondegenerate birational projections the ideal sheaf of the curve is (d2-b+1,d1-a+1)-regular. We also give an example showing that in some cases this bound is the best possible.
Lozovanu, V. (2009). Regularity of smooth curves in biprojective spaces. JOURNAL OF ALGEBRA, 322(7), 2355-2365 [10.1016/j.jalgebra.2009.07.013].
Regularity of smooth curves in biprojective spaces
LOZOVANU, VICTOR
2009
Abstract
Maclagan and Smith developed a multigraded version of Castelnuovo-Mumford regularity. Based on their de nition we will prove in this paper that for a smooth curve C inside biprojective space of bidegree (d1,d2) with nondegenerate birational projections the ideal sheaf of the curve is (d2-b+1,d1-a+1)-regular. We also give an example showing that in some cases this bound is the best possible.
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