2024/04/04 by Luigi Ferraro, Ferraro, Luigi, W. Frank Moore +1
Mathematics · #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2404.03601
Let (R,\mathfrakm,\Bbbk) be a regular local ring of dimension 3. Let I be a Gorenstein ideal of R of grade 3. It follows from a result of Buchsbaum and Eisenbud 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 \mathfrakm; we say that J is a trimming of I. In a previous work, the first author and A. Hardesty constructed an explicit free resolution of R/J and computed a DG algebra structure on this resolution. They utilized these products to analyze the Tor algebra of such trimmed ideals. Missing from their result was the case where I is five generated. In this paper we address this case.