Lifting tropical self intersections

Yoav Len, Matt Satriano

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We study the tropicalization of intersections of plane curves, under the assumption that they have the same tropicalization. We show that the set of tropical divisors that arise in this manner is a pure dimensional balanced polyhedral complex and compute its dimension. When the genus is at most 1, we show that all the tropical divisors that move in the expected dimension are realizable. As part of the proof, we introduce a combinatorial tool for explicitly constructing large families of realizable tropical divisors.

Original languageEnglish
Article number105138
Number of pages21
JournalJournal of Combinatorial Theory, Series A
Early online date4 Oct 2019
Publication statusPublished - Feb 2020


  • Tropical geometry
  • Intersection theory
  • Divisor theory
  • Chip-firing
  • Polyhedral complexes
  • Elliptic curves


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