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Transactions of the American Mathematical Society

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Curvilinear base points, local complete intersection and Koszul syzygies in biprojective spaces

Authors: J. William Hoffman and Hao Hao Wang
Journal: Trans. Amer. Math. Soc. 358 (2006), 3385-3398
MSC (2000): Primary 14Q10; Secondary 13D02, 14Q05
Published electronically: February 14, 2006
MathSciNet review: 2218980
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Abstract: Let $ I = \langle f_1 , f_2 , f_3\rangle$ be a bigraded ideal in the bigraded polynomial ring $ k[s, u; t, v]$. Assume that $ I$ has codimension 2. Then $ Z = \mathbb{V}(I) \subset \mathbf{P}^{1} \times \mathbf{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).

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Additional Information

J. William Hoffman
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803

Hao Hao Wang
Affiliation: Department of Mathematics, Southeast Missouri State University, Cape Girardeau, Missouri 63755

Keywords: Base points, local complete intersection, syzygy, saturation, projective space
Received by editor(s): May 19, 2003
Received by editor(s) in revised form: May 7, 2004
Published electronically: February 14, 2006
Additional Notes: The authors thank William Adkins and David Cox for numerous discussions and suggestions.
Article copyright: © Copyright 2006 American Mathematical Society

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