论文标题
38406501359372282063949及其所有：Fano问题的单曲
38406501359372282063949 & all that: Monodromy of Fano Problems
论文作者
论文摘要
FANO问题是一个列举的问题，即在$ \ Mathbb {p}^n $中的完整相交的$ r $维线性子空间计数，每当相应的fano方案是有限的时。一个经典的例子是在立方表面上枚举线。我们将有限的FANO计划的单片$ f_ {r}（x）$作为完整的交叉点$ x $变化。我们证明，在大多数情况下，单片组是对称或交替的。在特殊情况下，单片组是Weyl Groups $ W（E_6）$或$ W（D_K）$之一。
A Fano problem is an enumerative problem of counting $r$-dimensional linear subspaces on a complete intersection in $\mathbb{P}^n$ over a field of arbitrary characteristic, whenever the corresponding Fano scheme is finite. A classical example is enumerating lines on a cubic surface. We study the monodromy of finite Fano schemes $F_{r}(X)$ as the complete intersection $X$ varies. We prove that the monodromy group is either symmetric or alternating in most cases. In the exceptional cases, the monodromy group is one of the Weyl groups $W(E_6)$ or $W(D_k)$.
