The Tor Algebra of Trimmings of Gorenstein Ideals

Authors

Luigi Ferraro, The University of Texas Rio Grande Valley
Alexis Hardesty

Document Type

Article

Publication Date

12-13-2023

Abstract

Let (R,\mathfrak m,\Bbbk ) be a regular local ring of dimension 3. Let I be a Gorenstein ideal of R of grade 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 \mathfrak 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 \textbf{G} hold true in our context. Furthermore, we address the realizability question for ideals of class \textbf{G}.

Comments

Original published version available at https://doi.org/10.1007/s40306-023-00512-6

Recommended Citation

Ferraro, L., Hardesty, A. The Tor Algebra of Trimmings of Gorenstein Ideals. Acta Math Vietnam 48, 567–604 (2023). https://doi.org/10.1007/s40306-023-00512-6

Publication Title

Acta Math Vietnam

DOI

10.1007/s40306-023-00512-6