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.
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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