论文标题
代数和o最小流量超出了CoCompact案例
Algebraic and o-minimal flows beyond the cocompact case
论文作者
论文摘要
令$ x \ subset \ mathbb {c}^n $为代数品种，让$λ\ subset \ subset \ mathbb {c}^n $是一个离散的子组，其真实且复杂的跨度同意。我们描述了$ x $ in $ \ mathbb {c}^n /λ$的图像的拓扑封闭，从而在$λ$是cocompact的情况下扩展了Peterzil-Starchenko的结果。 当$ x \ subset \ mathbb {r}^n $在o最小结构中可以定义时，我们还获得了类似的扩展名，而对$λ$没有限制，并且作为应用程序证明了gallinaro的以下猜想：对于封闭的半代数$ x \ subset $ x \ subset \ mathbb {c} c}^n $（例如， $ \ exp：\ mathbb {c}^n \ to（\ mathbb {c}^*） $ \ mathbb {t} _i \ subset（\ mathbb {c}^*）^n $是正数紧凑型真实Tori和$ c_i \ subset \ subset \ mathbb {c}^n $是半algebraic。
Let $X \subset \mathbb{C}^n$ be an algebraic variety, and let $Λ\subset \mathbb{C}^n$ be a discrete subgroup whose real and complex spans agree. We describe the topological closure of the image of $X$ in $\mathbb{C}^n / Λ$, thereby extending a result of Peterzil-Starchenko in the case when $Λ$ is cocompact. We also obtain a similar extension when $X\subset \mathbb{R}^n$ is definable in an o-minimal structure with no restrictions on $Λ$, and as an application prove the following conjecture of Gallinaro: for a closed semi-algebraic $X\subset \mathbb{C}^n$ (such as a complex algebraic variety) and $\exp:\mathbb{C}^n\to (\mathbb{C}^*)^n$ the coordinate-wise exponential map, we have $\overline{\exp(X)}=\exp(X)\cup \bigcup_{i=1}^m \exp(C_i)\cdot \mathbb{T}_i$ where $\mathbb{T}_i\subset (\mathbb{C}^*)^n$ are positive-dimensional compact real tori and $C_i\subset \mathbb{C}^n$ are semi-algebraic.
