论文标题
通过ehrhart多项式对复杂的投影空间的一些特征
Some characterizations of the complex projective space via Ehrhart polynomials
论文作者
论文摘要
令$ p_ {λς_n} $为与标准symplex $σ_n\ subset \ subset \ mathbb {r}^n $相关的ehrhart多项式。在本文中，我们证明，如果$（m，l）$是$ n $二的两极化的复曲面，则具有相关的delzant polytope $δ$和ehrhart polyenmial $p_Δ$，以便$p_Δ=p_Δ=p_Δ= p _ {λς_n} $ （\ Mathbb {c} p^n，o（λ））$（其中$ o（1）$是$ \ mathbb {c} p^n $上的超平面捆绑包）在以下三种情况下：1。任意$ n $ and $ n $ and $λ= 1 $，2 $，2 $ n = 2 $ n = 2 $和$λ= 3 $，$λ chow可以半固定。
Let $P_{λΣ_n}$ be the Ehrhart polynomial associated to an intergal multiple $λ$ of the standard symplex $Σ_n \subset \mathbb{R}^n$. In this paper we prove that if $(M, L)$ is an $n$-dimensional polarized toric manifold with associated Delzant polytope $Δ$ and Ehrhart polynomial $P_Δ$ such that $P_Δ=P_{λΣ_n}$, for some $λ\in \mathbb{Z}^+$, then $(M, L)\cong (\mathbb{C} P^n, O(λ))$ (where $O(1)$ is the hyperplane bundle on $\mathbb{C} P^n$) in the following three cases: 1. arbitrary $n$ and $λ=1$, 2. $n=2$ and $λ=3$, 3. $λ=n+1$ under the assumption that the polarization $L$ is asymptotically Chow semistable.
