论文标题
投影线产品的高度重合
Height coincidences in products of the projective line
论文作者
论文摘要
我们考虑$（\ Mathbb {p}^1）^n $中的HyperSurfaces，该^n $在拆分映射方面包含一个通用的小动力高度序列，并将项目投影到$ N-1 $坐标上。我们表明，这些超曲面满足了其观点与零高度坐标之间的牢固巧合关系。更确切地说，它认为，在Zariski开放的密集子集中，这种超出表面$ N-1 $坐标的高度为零，并且仅当所有坐标的高度为零时。这是分解拆分图的动力学bogomolov猜想的分辨率的关键步骤。
We consider hypersurfaces in $(\mathbb{P}^1)^n$ that contain a generic sequence of small dynamical height with respect to a split map and project onto $n-1$ coordinates. We show that these hypersurfaces satisfy strong coincidence relations between their points with zero height coordinates. More precisely, it holds that in a Zariski-open dense subset of such a hypersurface $n-1$ coordinates have height zero if and only if all coordinates have height zero. This is a key step in the resolution of the dynamical Bogomolov conjecture for split maps.
