# Effective divisor classes on metric graphs

@article{Gross2022EffectiveDC, title={Effective divisor classes on metric graphs}, author={Andreas Gross and Farbod Shokrieh and Lilla T'othm'er'esz}, journal={Mathematische Zeitschrift}, year={2022} }

We introduce the notion of semibreak divisors on metric graphs (tropical curves) and prove that every effective divisor class (of degree at most the genus) has a semibreak divisor representative. This appropriately generalizes the notion of break divisors (in degree equal to genus). Our method of proof is new, even for the special case of break divisors. We provide an algorithm to efficiently compute such semibreak representatives. Semibreak divisors provide the tool to establish some basic…

## References

SHOWING 1-10 OF 34 REFERENCES

### Rank-determining sets of metric graphs

- Mathematics, Computer ScienceJ. Comb. Theory, Ser. A
- 2011

### Metric properties of the tropical Abel–Jacobi map

- Mathematics
- 2009

Let Γ be a tropical curve (or metric graph), and fix a base point p∈Γ. We define the Jacobian group J(G) of a finite weighted graph G, and show that the Jacobian J(Γ) is canonically isomorphic to the…

### Nonarchimedean geometry, tropicalization, and metrics on curves

- Mathematics
- 2011

We develop a number of general techniques for comparing analytifications and tropicalizations of algebraic varieties. Our basic results include a projection formula for tropical multiplicities and a…

### A note on Brill-Noether thoery and rank determining sets for metric graphs

- Mathematics
- 2011

We produce open subsets of the moduli space of metric graphs without separating edges where the dimensions of Brill-Noether loci are larger than the corresponding Brill-Noether numbers. These graphs…

### Tropical varieties for non-archimedean analytic spaces

- Mathematics
- 2007

Generalizing the construction from tropical algebraic geometry, we associate to every (irreducible d-dimensional) closed analytic subvariety of $\mathbb{G}_{m}^{n}$ a tropical variety in ℝn with…

### Lifting Divisors on a Generic Chain of Loops

- MathematicsCanadian Mathematical Bulletin
- 2015

Abstract Let $C$ be a curve over a complete valued field having an infinite residue field and whose skeleton is a chain of loops with generic edge lengths. We prove that any divisor on the chain of…

### The Skeleton of the Jacobian, the Jacobian of the Skeleton, and Lifting Meromorphic Functions From Tropical to Algebraic Curves

- Mathematics
- 2013

Let K be an algebraically closed field which is complete with respect to a nontrivial, non-Archimedean valuation and let \Lambda be its value group. Given a smooth, proper, connected K-curve X and a…