论文标题
Segre立方的四维表亲
A four-dimensional cousin of the Segre cubic
论文作者
论文摘要
该注释专用于特殊的Fano四倍，该曲线由五个变量的偏斜形式的四维空间定义。这四倍似乎与经典的Segre Cutic及其Cremona-Richmond的平面配置密切相关。除其他特殊属性外，它是无限的僵化，有第六名。我们展示了如何通过爆破和收缩来构造它，从四维二次的五个飞机的配置开始，与对称组$ s_5 $兼容。从这种结构中，我们能够明确描述Chow环。
This note is devoted to a special Fano fourfold defined by a four-dimensional space of skew-symmetric forms in five variables. This fourfold appears to be closely related with the classical Segre cubic and its Cremona-Richmond configuration of planes. Among other exceptional properties, it is infinitesimally rigid and has Picard number six. We show how to construct it by blow-up and contraction, starting from a configuration of five planes in a four-dimensional quadric, compatibly with the symmetry group $S_5$. From this construction we are able to describe the Chow ring explicitly.
