English

Tropical Linear Series and Tropical Independence

Algebraic Geometry 2022-10-03 v1

Abstract

We propose a definition of tropical linear series that isolates some of the essential combinatorial properties of tropicalizations of not-necessarily-complete linear series on algebraic curves. The definition combines the Baker-Norine notion of rank with the notion of tropical independence and has the property that the restriction of a tropical linear series of rank r to a connected subgraph is a tropical linear series of rank r. We show that tropical linear series of rank 1 are finitely generated as tropical modules and state a number of open problems related to algebraic, combinatorial, and topological properties of higher rank tropical linear series

Keywords

Cite

@article{arxiv.2209.15478,
  title  = {Tropical Linear Series and Tropical Independence},
  author = {David Jensen and Sam Payne},
  journal= {arXiv preprint arXiv:2209.15478},
  year   = {2022}
}