发表机构
Princeton University（普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用热带方法研究完备环面簇上Chern类平凡的环面向量丛，证明其可经特征标扭曲后由低维簇拉回，推广了Payne定理，并构造了无此类非平凡丛的例子，引入旗装饰作为关键工具。
AI 中文摘要
我们研究完备环面簇上全等变 Chern 类平凡的环面向量丛。我们的方法是热带性质的，使用了 Kaveh 和 Manon 引入的作为分段线性映射的热带环面向量丛的概念。我们证明，任何秩为 $r$、Chern 类平凡且等变 Chern 根仿射独立的环面向量丛，在乘以一个特征标后，等变同构于从有限个维数至多为 $r-1$ 的簇中的某一个拉回的环面向量丛。这推广了 Payne 关于秩 $r\leq 3$ 且 Chern 类平凡的环面向量丛的一个定理。作为应用，我们构造了维数为 $n$ 的完备环面簇的例子，这些簇不承认任何秩 $r\leq n+1$ 且具有上述性质的非平凡环面向量丛。我们还引入了我们称之为置换多面体的旗装饰的组合对象，其凸性性质对我们的结果至关重要。
英文摘要
We study toric vector bundles on complete toric varieties whose total equivariant Chern classes are trivial. Our approach is tropical, using the notion of tropical toric vector bundles as piecewise linear maps introduced by Kaveh and Manon. We prove that any toric vector bundle of rank $r$ with trivial Chern class and affinely independent equivariant Chern roots is equivariantly isomorphic to a toric vector bundle pulled back from one of a finite set of varieties with dimension at most $r-1$ after twisting by a character. This extends a theorem of Payne about toric vector bundles of rank $r\leq 3$ with trivial Chern class. As an application, we construct examples of complete toric varieties of dimension $n$ that admit no nontrivial toric vector bundles of rank $r\leq n+1$ with the aforementioned properties. We also introduce combinatorial gadgets we call flag decorations of permutohedra, whose convexity properties are key for our results.
Comments24 pages; comments are welcome
