论文标题
Fano的最后一个Fano
Fano's Last Fano
论文作者
论文摘要
1949年，Fano发表了他的最后一篇论文，上面写着$ 3 $ folds，带有规范的部分曲线。在那里，他构建并描述了$ x^{22} _3 $ in $ {\ Mathbb p}^{13} $的$ 3 $ fold，并用规范曲线部分，我们喜欢将其称为Fano的最后一个Fano。我们报告了Fano的构建，以现代语言提供了各种证明（我们认为缺少）证明，并试图使用当时可用的结果和技术。然后，我们使用现代工具构建Fano的，特别是通过在理性表面上的零周期的希尔伯特方案构建。结果，我们很容易地指出了Mori-Mukai分类中的相应示例。
In 1949 Fano published his last paper on $3$-folds with canonical sectional curves. There he constructed and described a $3$-fold of the type $X^{22}_3$ in ${\mathbb P}^{13}$ with canonical curve section, which we like to call Fano's last Fano. We report on Fano's construction, providing various (in our opinion missing) proofs, in modern language and trying to use results and techniques available at that time. Then we construct Fano's with modern tools, in particular via the Hilbert scheme of zero cycles on a rational surface; as a consequence we easily point out the corresponding example in the Mori-Mukai classification.
