发表机构
University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明正定二次型非负余范等价于其为拟阵型，解决了相关猜想，还将热带肖特基轨迹的判定转化为余图拟阵的判定，为任意亏格的热带肖特基问题提供了算法。
AI 中文摘要
我们证明了一个正定二次型具有非负余范当且仅当它是拟阵型的，解决了Dutour Sikirić和Kummer提出的猜想。我们表明，正余范支撑集确定了一个正则拟阵，且正余范是该二次型的单模整系数分解的系数。据此，我们证明一个正定二次型属于热带肖特基轨迹当且仅当它的余范非负且其正余范支撑拟阵是余图的。这回答了Chua、Kummer和Sturmfels提出的问题，并为任意亏格的热带肖特基判定与恢复问题提供了算法。
英文摘要
We prove that a positive-definite quadratic form has nonnegative conorms if and only if it is matroidal, resolving a conjecture of Dutour Sikirić and Kummer. We show that the positive conorm support determines a regular matroid, and the positive conorms are the coefficients of a unimodular integral decomposition of the form. As a result, we show that a positive-definite form lies in the tropical Schottky locus if and only if its conorms are nonnegative and its positive conorm support matroid is cographic. This answers a question of Chua, Kummer, and Sturmfels and provides algorithms for the tropical Schottky decision and recovery problems in every genus.
Comments18 pages, comments welcome!
