Tropical complexes
arXiv:1308.3813 · doi:10.1007/s00229-019-01148-3
Abstract
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.
37 pages, 5 figures. v2: Sections 5-6 now appear in arXiv:1506.02023 and Section 7 in arXiv:1511.00650. v3: Rewritten, definition of Weil divisors on tropical complexes of dimension at least 3 changed slightly. v4: Many improvements in the exposition