The Tor algebra of trimmings of Gorenstein ideals




Ferraro, Luigi
Hardesty, Alexis

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Let (R,m,k) be a regular local ring of dimension 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric matrix of odd size such that I is generated by the sub-maximal pfaffians of this matrix. Let J be the ideal obtained by multiplying some of the pfaffian generators of I by m; we say that J is a trimming of I. Building on a recent paper of Vandebogert, we construct an explicit free resolution of R=J and compute a partial DG algebra structure on this resolution. We provide the full DG algebra structure in the appendix. We use the products on this resolution to study the Tor algebra of such trimmed ideals and we use the information obtained to prove that recent conjectures of Christensen, Veliche and Weyman on ideals of class G hold true in our context. Furthermore, we address the realizability question for ideals of class G.


Article originally published by Acta Mathematica Vietnamica. English. Published 2023.
File has been archived under a 12-month publisher-required embargo. File will become available December 1, 2024.


Pfaffian, Trimming, Gorenstein, DG algebra, Free resolution


This is the post-print version of an article that is available at Recommended citation: Ferraro, L., & Hardesty, A. (2023b). The Tor algebra of trimmings of Gorenstein ideals. Acta Mathematica Vietnamica. This item has been deposited in accordance with publisher copyright and licensing terms and with the author’s permission.