论文标题
Gorenstein理想的三个三角形的Tor代数
The Tor algebra of trimmings of Gorenstein ideals
论文作者
论文摘要
令$（r，\ m athfrak {m}，\ bbbk）$为常规的尺寸3。让$ i $是3级$ r $ 3级的戈伦斯坦理想。Buchsbaum和eisenbud证明了奇特大小的奇怪尺寸，因此由$ i $ i $ i $ maximians产生了submaximians matrix at matrix at rik a pfff f f。让$ j $是通过将$ i $的一些Pfaffian发电机乘以$ \ mathfrak {m} $获得的理想选择。我们说$ j $是$ i $的修剪。在最近的Vandebogert论文的基础上，我们构建了$ r/j $的明确免费分辨率，并根据该决议计算部分DG代数结构。我们在附录中提供完整的DG代数结构。我们使用该决议上的产品来研究这种修剪理想的Tor代数，并使用获得的信息来证明Christensen，Veliche和Weyman最近对$ \ MathBf {G g} $的理想的猜想在我们的背景下保持真实。此外，我们解决了类$ \ mathbf {g} $的理想的可靠性问题。
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 $\mathbf{G}$ hold true in our context. Furthermore, we address the realizability question for ideals of class $\mathbf{G}$.
