Lifting tropical self intersections

Yoav Len, Matt Satriano

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
1 Downloads (Pure)

Abstract

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
Volume170
Early online date4 Oct 2019
DOIs
Publication statusPublished - Feb 2020

Keywords

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

Fingerprint

Dive into the research topics of 'Lifting tropical self intersections'. Together they form a unique fingerprint.

Cite this