Local Complete Intersections in P^2 and Koszul Syzygies

Simple item page
dc.creatorCox, David
dc.creatorSchenck, Hal
dc.date2001-10-09
dc.date.accessioned2026-07-07T04:43:44Z
dc.date.available2026-07-07T04:43:44Z
dc.descriptionWe study the syzygies of a codimension two ideal I = <f_1,f_2,f_3> in 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. When I is saturated, we relate our theorem to results of Weyman and of Simis and Vasconcelos. We conclude with an example of how our theorem fails for four generated local complete intersections in k[x,y,z] and we discuss generalizations to higher dimensions.
dc.description8 pages, LaTeX2e using amsart documentclass
dc.identifierhttps://arxiv.org/abs/math/0110097
dc.identifierhttp://arxiv.org/abs/math/0110097
dc.identifierProc. Amer. Math. Soc. 131 (2003), 2007--2014
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62354
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subjectPrimary 14Q10; Secondary 13D02, 14Q05, 65D17
dc.titleLocal Complete Intersections in P^2 and Koszul Syzygies
dc.typetext

Files

Collections

arXiv