论文标题
通过Gröbner变性检测Golodness
Detecting Golodness via Gröbner Degeneration
论文作者
论文摘要
在本文中，我们研究了可以沿DG代数的形态转移戈洛德的程度。特别是，我们表明，如果$ i $是所谓的纤维不变理想，那么$ i $的golodness等同于Golodness的最初理想$ i $。我们将其用于将单一理想的Golodness结果传递到更一般的理想类别。我们还证明，任何带有线性分辨率的所谓彩虹单一理想都定义了Golod环。该结果涵盖并概括了许多已知的Golodness结果，用于单一理想的类别。然后，我们结合了开发的技术，以简化证据，即（稀疏）通用矩阵的最大未成年人定义了Golod环，独立于特征。
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.
