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# Local Complete Intersections in P 2 and Koszul Syzygies

@inproceedings{CoxLocalCI, title={Local Complete Intersections in P 2 and Koszul Syzygies}, author={David Cox and Hal Schenck} }

We study the syzygies of a codimension two ideal I = f 1 , f 2 , f 3 ⊆ k[x, y, z]. Our main result is that the module of syzygies vanishing (scheme-theoretically) at the zero locus Z = V(I) is generated by the Koszul syzygies iff Z is a local complete intersection. The proof uses a characterization of complete intersections due to Herzog [4]. When I is saturated, we relate our theorem to results of Weyman [7] and Simis and Vasconcelos [6]. We conclude with an example of how our theorem fails… CONTINUE READING