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Tropical complexes. (English) Zbl 1454.14154

Summary: 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.

MSC:

14T15 Combinatorial aspects of tropical varieties
14D06 Fibrations, degenerations in algebraic geometry
14T20 Geometric aspects of tropical varieties
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