Let $C \subset P^{g-1}$ be a smooth canonical curve of genus $g \geq 3$. Thepurpose of this article is to further develop a method to classify varietieshaving $C$ as their curve section, using Gaussian map computations. In aprevious article a careful analysis of the degeneration to the cone over thehyperplane section was made for _prime_ Fano threefolds, that is Fanothreefolds whose Picard group is generated by the hyperplane bundle. In thisarticle we extend this method and classify Fano threefolds of higher index(which still have Picard number one). We are also able to classify Mukaivarieties, i.e. varieties of dimension four or more with canonical curvesections.
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机译：令$ C \ subset P ^ {g-1} $是$ g \ geq 3 $属的光滑典范曲线。本文的目的是进一步开发一种方法，使用高斯映射计算将具有$ C $作为其曲线截面的品种分类。在上一篇文章中，对Fano的三倍折叠，即超平面截面上圆锥的退化进行了仔细的分析，这就是Fanothreefolds，其Picard基团是由超平面束产生的。在本文中，我们扩展了该方法并将Fano的三倍高索引分类（仍然具有Picard第一）。我们还能够对Mukai变量进行分类，即具有规范曲线截面的4维或4维以上的变体。
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