通过Gröbner退化检测Goldness
Detecting Golodness via Gröbner Degeneration
摘要：
本文研究了DG-代数的Goldness在何种程度上可以沿着态射转移。特别是，我们表明，如果$I$是一个所谓的纤维不变的理想，那么Goldness的$I$是等价的Goldness的初始理想的$I$。我们用它来转移Goldness结果单项理想更一般的理想类。我们还证明了任何所谓的彩虹单项式理想与线性分辨率定义的Golod环，这一结果包括和推广了许多已知的Golodness结果类的单项式理想。然后，我们结合开发的技术，给出一个简洁的证明，最大未成年人（稀疏）通用矩阵定义的Golod环，独立的特征。
英文摘要：
In this paper we study the extent to which Golodness may be transferred along morphisms of DG-algebras. In particular, we show that if $I$ is a so-called fiber invariant ideal, then Golodness of $I$ is equivalent to Golodness of the initial ideal of $I$. We use this to transfer Golodness results for monomial ideals to more general classes of ideals. We also prove that any so-called rainbow monomial ideal with linear resolution defines a Golod ring; this result encompasses and generalizes many known Golodness results for classes of monomial ideals. We then combine the techniques developed to give a concise proof that maximal minors of (sparse) generic matrices define Golod rings, independent of characteristic.
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