Let X ⊆ ℙN be a non-degenerate normal projective variety of codimension e and degree d with isolated ℚ-Gorenstein singularities. We prove that the Castelnuovo–Mumford regularity reg(𝒪X) ≤ d − e, as predicted by the Eisenbud–Goto regularity conjecture. Such a bound fails for general projective varieties by a recent result of McCullough–Peeva. The main techniques are Noma’s classification of non-degenerate projective varieties and Nadel vanishing for multiplier ideals. We also classify the extremal and the next to extremal cases.

中文翻译：

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孤立奇点品种结构滑轮的规律性

让X ⊆ ℙñ是余维的非退化正规射影变体e和学位d与隔离ℚ-Gorenstein 奇点。我们证明了 Castelnuovo-Mumford 规律注册(𝒪X) ≤ d - e，正如 Eisenbud-Goto 正则性猜想所预测的那样。根据 McCullough-Peeva 最近的一个结果，对于一般射影变体，这种界限失败了。主要技术是 Noma 的非退化射影簇分类和乘数理想的 Nadel 消失。我们还对极值和次极值情况进行分类。