Perfect ideals of grade three defined by skew-symmetrizable matrices
Bull. Korean Math. Soc. 2012 Vol. 49, No. 4, 715-736
Printed July 1, 2012
Yong Sung Cho, Oh-Jin Kang, and Hyoung June Ko
Yonsei University, University of Incheon, Yonsei University
Abstract : Brown provided a structure theorem for a class of perfect ideals of grade 3 with type 2 and $\lambda >0.$ We introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4 in a Noetherian local ring. We construct a class of perfect ideals $I$ of grade 3 with type 2 defined by a certain skew-symmetrizable matrix. We present the Hilbert function of the standard $k$-algebras $R/I,$ where $R$ is the polynomial ring $R=k[v_0, v_1, \ldots, v_m]$ over a field $k$ with indeterminates $v_i$ and $\deg v_i=1.$
Keywords : almost complete intersection of grade 3, perfect ideal of grade 3, minimal free resolution, linkage
MSC numbers : 13C05, 13H10, 13C02, 13C40
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