标题： Fano 族的次最大初等对称函数 显示英文标题

标题： Fano schemes of sub-maximal elementary symmetric functions

摘要： Denote by $E_r$ the $r^{th}$ elementary symmetric polynomial in $\dim V$ variables for a vector space $V$ over an infinite field $\Bbbk$. 我们描述了在 $F_{d-1}(Z(E_{\dim V-1}))$ 的有理点，这是包含在 $E_{\dim V-1}$ 零点中的射影 $(d-1)$-空间的 Fano 模式。孤立点仅在 $\dim V=2d$ 时存在，在这种情况下，它们与一个 $2d$-元素集合上的 $1\cdot 3\cdots (2d-1)$ 配对一一对应。这特别证实了 Ambartsoumian、Auel 和 Jebelli 的一个猜想，即（在 $\mathbb{R}$ 上）所有孤立点都可以通过适当的符号的积分星变换恢复。 显示英文摘要

摘要： Denote by $E_r$ the $r^{th}$ elementary symmetric polynomial in $\dim V$ variables for a vector space $V$ over an infinite field $\Bbbk$. We describe the rational points on the Fano scheme $F_{d-1}(Z(E_{\dim V-1}))$ of projective $(d-1)$-spaces contained in the zero locus of $E_{\dim V-1}$. Isolated points exist precisely for $\dim V=2d$, in which case they are in bijection with the $1\cdot 3\cdots (2d-1)$ pairings on a $2d$-element set. This, in particular, confirming a conjecture of Ambartsoumian, Auel and Jebelli to the effect that (over $\mathbb{R}$) all isolated points are recoverable via integral star transforms with appropriate symbols.