English

Refined count for rational tropical curves in arbitrary dimension

Algebraic Geometry 2021-03-24 v5

Abstract

In this paper we introduce a refined multiplicity for rational tropical curves in arbitrary dimension, which generalizes the refined multiplicity introduced by F. Block and L. G\"ottsche in arXiv:1407.2901 . We then prove an invariance statement for the count of rational tropical curves in several enumerative problems using this new refined multiplicity. This leads to the definition of Block-G\"ottsche polynomials in any dimension.

Keywords

Cite

@article{arxiv.2010.05777,
  title  = {Refined count for rational tropical curves in arbitrary dimension},
  author = {Thomas Blomme},
  journal= {arXiv preprint arXiv:2010.05777},
  year   = {2021}
}

Comments

32 pages + 6 pages of appendix. References added and typos corrected

R2 v1 2026-06-23T19:16:52.546Z