English

Complex and tropical counts via positive characteristic

Algebraic Geometry 2020-04-03 v1

Abstract

We reconcile the discrepancy between the complex and tropical counts of some enumerative problems reducing to positive characteristic. Each problem that we consider suggests a prime with special behaviour. Modulo this prime, the solutions coalesce in uniform clusters: at this special prime, the geometric and the tropical behaviours match. As examples, we concentrate on inflection points of plane curves and theta-hyperplanes of canonical curves.

Keywords

Cite

@article{arxiv.2004.00955,
  title  = {Complex and tropical counts via positive characteristic},
  author = {Marco Pacini and Damiano Testa},
  journal= {arXiv preprint arXiv:2004.00955},
  year   = {2020}
}

Comments

18 pages

R2 v1 2026-06-23T14:36:39.607Z