论文标题
一些fano歧管，其Hilbert多项式完全可以降低于$ \ Mathbb Q $
Some Fano manifolds whose Hilbert polynomial is totally reducible over $\mathbb Q$
论文作者
论文摘要
令$（x，l）$为任何fano歧管，其基本除数的正倍元$ h $。定义$（x，l）$的Hilbert曲线的多项式归结为$（x，h）$的Hilbert多项式，因此，它完全可以降低到$ \ Mathbb c $上；此外，分解中出现的一些线性因子具有有理系数，例如如果$ x $具有索引$ \ geq 2 $。自然要问所有线性因素何时发生同样的情况。在这里，研究了三种特殊类型的Fano歧管的希尔伯特多项式的$ \ Mathbb Q $的总降低性：大型索引的Fano歧管，低维的曲曲弹歧管和低coIndex的Fano捆绑包。
Let $(X,L)$ be any Fano manifold polarized by a positive multiple of its fundamental divisor $H$. The polynomial defining the Hilbert curve of $(X,L)$ boils down to being the Hilbert polynomial of $(X,H)$, hence it is totally reducible over $\mathbb C$; moreover, some of the linear factors appearing in the factorization have rational coefficients, e.g. if $X$ has index $\geq 2$. It is natural to ask when the same happens for all linear factors. Here the total reducibility over $\mathbb Q$ of the Hilbert polynomial is investigated for three special kinds of Fano manifolds: Fano manifolds of large index, toric Fano manifolds of low dimension, and Fano bundles of low coindex.
