Algebraic intersections on Bouw-Möller surfaces, and more general convex polygons

Julien Boulanger, Irene Pasquinelli
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Abstract

This paper focuses on intersection of closed curves on translation surfaces. Namely, we investigate the question of determining the intersection of two closed curves of a given length on such surfaces. This question has been investigated in several papers and this paper complement the work of Boulanger, Lanneau and Massart done for double regular polygons, and extend the results to a large family of surfaces which includes in particular Bouw-M\"oller surfaces. Namely, we give an estimate for KVol on surfaces based on geometric constraints (angles and indentifications of sides). This estimate is sharp in the case of Bouw-M\"oller surfaces with a unique singularity, and it allows to compute KVol on the $SL_2(\mathbb{R})$-orbit of such surfaces.
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布沃-莫勒曲面上的代数相交,以及更一般的凸多边形
本文主要研究平移面上闭合曲线的交点。也就是说,我们研究的问题是如何确定平移面上给定长度的两条闭合曲线的交点。这个问题已经在多篇论文中进行了研究,本文是对布兰杰、朗诺和马萨特针对双正多边形所做工作的补充,并将结果扩展到了一个庞大的曲面家族,其中特别包括 Bouw-M\"oller 曲面。这个估计值在具有唯一奇点的布瓦-莫勒曲面的情况下是尖锐的,它允许计算这类曲面的$SL_2(\mathbb{R})$轨道上的KVol。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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