English

Real enumerative invariants relative to the toric boundary and their refinement

Algebraic Geometry 2025-04-22 v2

Abstract

We introduce new invariants of a class of toric surfaces (including the projective plane) that arise from appropriate enumeration of real curves of genus one and two. These invariants admit a refinement similar to the one introduced by Grigory Mikhalkin in the rational case.

Keywords

Cite

@article{arxiv.2401.06718,
  title  = {Real enumerative invariants relative to the toric boundary and their refinement},
  author = {Ilia Itenberg and Eugenii Shustin},
  journal= {arXiv preprint arXiv:2401.06718},
  year   = {2025}
}

Comments

This is a substantially revised version: two signed counts of real curves of genus 0, 1, and 2 are introduced, both giving real enumerative invariants; two extremal cases are excluded from the main theorems