论文标题
地层$ \ MATHCAL {H}（2）$中翻译表面的代数交叉点
Algebraic intersection for translation surfaces in the stratum $\mathcal{H}(2)$
论文作者
论文摘要
我们研究了定义为至上的数量$ \ mbox {kvol} $，在所有对封闭曲线上，其代数交集，除以其长度的乘积，时代的面积为表面面积。我们认为我们认为的表面在级别$ \ mathcal {h}（2）$ $ 2 $的翻译表面，一个圆锥点。我们提供了一个明确的序列$ l（n，n）$的表面，使得$ \ mbox {kvol}（l（n，n，n））\ longrightarrow 2 $ 2 $当$ n $转到无限时，$ 2 $是$ \ mbox {kvol} $ the $ \ mbox {kvol} $ over $ \ \ \ \ \ \ \ \ mathcal {kvol} $。
We study the quantity $\mbox{KVol}$ defined as the supremum, over all pairs of closed curves, of their algebraic intersection, divided by the product of their lengths, times the area of the surface. The surfaces we consider live in the stratum $\mathcal{H}(2)$ of translation surfaces of genus $2$, with one conical point. We provide an explicit sequence $L(n,n)$ of surfaces such that $\mbox{KVol}(L(n,n)) \longrightarrow 2$ when $n$ goes to infinity, $2$ being the conjectured infimum for $\mbox{KVol}$ over $\mathcal{H}(2)$.
