Papers › Higher structure maps for free resolutions of length 3 and linkage
Higher structure maps for free resolutions of length 3 and linkage
Lorenzo Guerrieri, Xianglong Ni, Jerzy Weyman
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Let I be a perfect ideal of height 3 in a Gorenstein local ring R. Let 𝔽 be the minimal free resolution of I. A sequence of linear maps, which generalize the multiplicative structure of 𝔽, can be defined using the generic ring associated to the format of 𝔽. Let J be an ideal linked to I. We provide formulas to compute some of these maps for the free resolution of J in terms of those of the free resolution of I. We apply our results to describe classes of licci ideals, showing that a perfect ideal with Betti numbers (1,5,6,2) is licci if and only if at least one of these maps is nonzero modulo the maximal ideal of R.
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