Curvilinear base points, local complete intersection and Koszul syzygies in biprojective spaces
Let I = 〈f 1, f 2, f 3〉 be a bigraded ideal in the bigraded polynomial ring k[s,u; t, v]. Assume that I has codimension 2. Then Z = V(I) ⊂ P 1 × P 1 is a finite set of points. We prove that if Z is a local complete intersection, then any syzygy of the f i vanishing at Z, and in a certain degree range, is in the module of Koszul syzygies. This is an analog of a recent result of Cox and Schenck (2003). © 2006 American Mathematical Society.
Publication Source (Journal or Book title)
Transactions of the American Mathematical Society
William Hoffman, J., & Wang, H. (2006). Curvilinear base points, local complete intersection and Koszul syzygies in biprojective spaces. Transactions of the American Mathematical Society, 358 (8), 3385-3398. https://doi.org/10.1090/S0002-9947-06-04119-5