发表机构
Graduate School of Science, Kyoto University（京都大学大学院理学研究科）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明热带松阪准则与热带松阪-兰准则，结合热带庞加莱公式为热带肖特基问题提供几何解，还开发了相关工具并回答了Brannetti等人的问题。
AI 中文摘要
热带肖特基问题询问哪些主极化热带阿贝尔簇与配备典范主极化的热带雅可比簇同构。本文证明了作为主要结果的热带松阪准则和热带松阪-兰准则，并表明它们的假设等价。结合Gross-Shokrieh证明的热带庞加莱公式，这些结果为热带肖特基问题提供了几何解决方案，特别对Brannetti-Melo-Viviani提出的问题给出了肯定回答。为证明两个准则开发了若干工具，其中包括建立热带阿贝尔簇上丰富热带除子的霍奇型不等式，以及证明主极化热带阿贝尔簇的分裂准则。
英文摘要
The tropical Schottky problem asks which principally polarized tropical abelian varieties are isomorphic to tropical Jacobian varieties equipped with their canonical principal polarizations. We prove the tropical Matsusaka criterion and the tropical Matsusaka--Ran criterion, which are the main results of this paper, and show that their hypotheses are equivalent. Together with the tropical Poincaré formula proved by Gross--Shokrieh, these results give a geometric solution to the tropical Schottky problem. In particular, we give an affirmative answer to a question posed by Brannetti--Melo--Viviani. Several tools are developed for the proofs of the two criteria. In particular, we establish Hodge-type inequalities for ample tropical Cartier divisors on tropical abelian varieties and prove a splitting criterion for principally polarized tropical abelian varieties.
Comments50 pages
