We introduce tropical complexes, as an enrichment of the dual complex of a degeneration with additional data from non-transverse intersection numbers. We define cycles, divisors, and linear equivalence on tropical complexes, analogous both to the corresponding theories on algebraic varieties and to previous work on graphs and abstract tropical curves. In addition, we establish conditions for the divisor-curve intersection numbers on a tropical complex to agree with the generic fiber of a degeneration.

中文翻译：

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热带复合体

我们引入了热带复合体，作为退化对偶复合体的丰富，具有来自非横向交叉点数的附加数据。我们定义了热带复形上的循环、除数和线性等价，类似于相应的代数变体理论以及之前关于图形和抽象热带曲线的工作。此外，我们为热带复合体上的除数曲线交点数建立了条件，以与退化的一般纤维一致。