论文标题
公制图上的主要捆绑包：$ \ mathrm {gl} _n $ case
Principal bundles on metric graphs: the $\mathrm{GL}_n$ case
论文作者
论文摘要
使用还原组$ g $的根基准的概念，我们建议在公制图上对主要$ g $ undle的热带类似物。我们专注于$ g = \ mathrm {gl} _n $，即向量捆绑包的情况。在这里，我们从多元阶段进行了矢量束的表征，并使用此描述证明了Weil-riemann-Roch Theorem和Narasimhan-seShadri对应关系的类似物。我们通过研究热带化过程进行。特别是，我们表明，泰特曲线上可半介载量捆绑包的模量空间的非架构骨架与其双重度量图上的半固定热带矢量捆绑包的模量空间的某个组成部分是同构的。
Using the notion of a root datum of a reductive group $G$ we propose a tropical analogue of a principal $G$-bundle on a metric graph. We focus on the case $G=\mathrm{GL}_n$, i.e. the case of vector bundles. Here we give a characterization of vector bundles in terms of multidivisors and use this description to prove analogues of the Weil--Riemann--Roch theorem and the Narasimhan--Seshadri correspondence. We proceed by studying the process of tropicalization. In particular, we show that the non-Archimedean skeleton of the moduli space of semistable vector bundles on a Tate curve is isomorphic to a certain component of the moduli space of semistable tropical vector bundles on its dual metric graph.
