English

Positivity of tropical multidegrees

Algebraic Geometry 2024-05-24 v2

Abstract

We define the multidegrees of a tropical variety. We prove that the positivity of a multidegree of a certain tropical variety is governed by the dimensions of the images of the tropical variety under suitable projection maps. As an application, we give a tropical proof of the criterion of the positivity of the multidegrees of a closed subscheme of a multi-projective space, originally proved by Castillo et al.

Keywords

Cite

@article{arxiv.2306.10589,
  title  = {Positivity of tropical multidegrees},
  author = {Xiang He},
  journal= {arXiv preprint arXiv:2306.10589},
  year   = {2024}
}

Comments

Slight change of terminology. Final version, accepted to Selecta Mathematica

R2 v1 2026-06-28T11:08:17.162Z