AI 中文总结
本文研究环面簇子簇上环面度量的非阿基米德Monge-Ampère测度，利用热带芽与热带格林函数显式描述其局部结构，推广热带相交积，为阿贝尔簇情形提供环面类比。
AI 中文摘要
我们研究环面簇的闭子簇上环面度量的非阿基米德Monge-Ampère测度，必要时先将问题归结到包含该子簇的最小环面轨道闭包上。该测度在环面边界上为零，且支撑在热带骨架上。我们的主要结果利用子簇的热带芽和度量的热带格林函数明确描述了其局部结构。更精确地说，热带化的Monge-Ampère测度是相应的多面体Monge-Ampère测度，它推广了热带相交积，而原始测度则通过从显式的热带与凸数据出发的热带拉回在局部恢复。这为阿贝尔簇子簇的类似结果提供了环面类比，并因热带化而出现新的局部现象。
英文摘要
We study non-archimedean Monge-Ampère measures of toric metrics on closed subvarieties of toric varieties, after reducing, if necessary, to the minimal torus-orbit closure containing the subvariety. The measure vanishes on the toric boundary and is supported on the tropical skeleton. Our main result explicitly describes their local structure in terms of the tropical germ of the subvariety and the tropical Green function of the metric. More precisely, the tropicalized Monge-Ampère measure is the corresponding polyhedral Monge-Ampère measure, which extends the tropical intersection product, while the original measure is recovered locally by tropical pullback from explicit tropical and convex data. This provides a toric counterpart to analogous results for subvarieties of abelian varieties, with new local phenomena arising from tropicalization.
