English

Refined count of real oriented rational curves

Algebraic Geometry 2021-07-16 v1

Abstract

We introduce a \textit{quantum index} for oriented real curves inside toric varieties. This quantum index is related to the computation of the area of the amoeba of the curve for some chosen 2-form. We then make a refined signed count of oriented real rational curves solution to some enumerative problem. This generalizes the results from G. Mikhalkin arXiv:1505.04338 to higher dimension. Finally, we use the tropical approach to relate these new refined invariants to previously known tropical refined invariants.

Keywords

Cite

@article{arxiv.2107.07286,
  title  = {Refined count of real oriented rational curves},
  author = {Thomas Blomme},
  journal= {arXiv preprint arXiv:2107.07286},
  year   = {2021}
}

Comments

37 pages, 1 figure

R2 v1 2026-06-24T04:13:38.416Z