We construct some new deformation families of four-dimensional Fano manifolds of index one in some known classes of Gorenstein formats. These families have explicit descriptions in terms of equations, defining their image under the anticanonical embedding in some weighted projective space. They also have relatively smaller anticanonical degree than most other known families of smooth Fano 4-folds.

中文翻译：

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GORENSTEIN 格式的平滑 FANO 4 折

我们在一些已知的 Gorenstein 格式类别中构建了一些新的四维 Fano 流形的变形族，索引为 1。这些族在方程方面有明确的描述，在一些加权投影空间中的反规范嵌入下定义它们的图像。与大多数其他已知的平滑 Fano 4 倍家族相比，它们的反规范度也相对较小。