In this article, we construct some examples of noncommutative projective Calabi–Yau schemes by using noncommutative Segre products and quantum weighted hypersurfaces. We also compare our constructions with commutative Calabi–Yau varieties and examples constructed in Kanazawa (2015, Journal of Pure and Applied Algebra 219, 2771–2780). In particular, we show that some of our constructions are essentially new examples of noncommutative projective Calabi–Yau schemes.

中文翻译：

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非交换射影 Calabi-Yau 方案的一些示例

在本文中，我们通过使用非交换 Segre 产品和量子加权超曲面构造了一些非交换射影 Calabi-Yau 方案的示例。我们还将我们的构造与交换 Calabi-Yau 簇以及在金泽构造的示例进行了比较（2015 年，纯粹与应用代数杂志219, 2771–2780）。特别是，我们表明我们的一些构造本质上是非交换射影卡拉比-丘方案的新例子。