On refined count of rational tropical curves

Eugenii Shustin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We address the problem of existence of refined (i.e., depending on a formal parameter) tropical enumerative invariants, and we present two new examples of a refined count of rational marked tropical curves. One of the new invariants counts plane rational tropical curves with an unmarked vertex of arbitrary valency. It was motivated by the tropical enumeration of plane cuspidal tropical curves given by Y. Ganor and the author, which naturally led to consideration of plane tropical curves with an unmarked four-valent vertex. Another refined invariant counts rational tropical curves of a given degree in the Euclidean space of arbitrary dimension matching specific constraints, which make the spacial refined invariant similar to known planar invariants.

Original languageEnglish
Pages (from-to)1027-1052
Number of pages26
JournalPure and Applied Mathematics Quarterly
Issue number4
StatePublished - 2020


  • Plane tropical curve
  • Rational tropical curve
  • Refined enumerative invariants
  • Spacial tropical curve
  • Tropical enumerative geometry


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