Let $A$ be the twisted commutative algebra freely generated by $d$ indeterminates of degree 1. We show that the regularity of an $A$‐module can be bounded from the first $\lfloor \frac{1}{4}{d}^2\rfloor +2$ terms of its minimal free resolution. This partially extends results of Church and Ellenberg from the $d=1$ case.

中文翻译：

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交换交换代数的正则界

让 $\mathrm{一种}$ 是自由生成的扭曲可交换代数 $d$ 不确定度1。我们证明 $\mathrm{一种}$-模块可以从第一个边界 $\lfloor \frac{\mathrm{1个}}{4}{d}^2\rfloor +2$最小的免费解决方案。这部分地扩展了Church和Ellenberg从$d=\mathrm{1个}$ 案件。