论文标题
混合曲线I的模量I：规范措施的变化
Moduli of hybrid curves I: Variations of canonical measures
论文作者
论文摘要
本文是专门研究Riemann表面及其模量空间的渐近几何形状的系列文章。 我们介绍了混合曲线的模量空间，作为曲线模量空间的新紧凑型，并完善了Deligne和Mumford获得的曲线。这是多尺寸几何对象的模量空间，它们混合了复杂和较高的热带和非架构的几何形状，反映了离散和连续特征。 我们在杂种曲线上定义了规范测量，这些测量将Arakelov-Bergman的衡量标准衡量，并在Riemann表面和张措施上进行度量。 然后，我们表明，该模量空间上的普遍测量的杂种曲线的通用家族连续变化。这提供了非安置的张措施与Riemann表面家族中Arakelov-Bergman量度的变化之间的确切联系，回答了一个问题以来Zhang在90年代接受可允许的配对的开创性工作以来就已经开了的问题。
The present paper is the first in a series devoted to the study of asymptotic geometry of Riemann surfaces and their moduli spaces. We introduce the moduli space of hybrid curves as a new compactification of the moduli space of curves, refining the one obtained by Deligne and Mumford. This is the moduli space for multiscale geometric objects which mix complex and higher rank tropical and non-Archimedean geometries, reflecting both discrete and continuous features. We define canonical measures on hybrid curves which combine and generalize Arakelov-Bergman measures on Riemann surfaces and Zhang measures on metric graphs. We then show that the universal family of canonically measured hybrid curves over this moduli space varies continuously. This provides a precise link between the non-Archimedean Zhang measure and variations of Arakelov-Bergman measures in families of Riemann surfaces, answering a question which has been open since the pioneering work of Zhang on admissible pairing in the nineties.
