Lifting divisors with imposed ramifications on a generic chain of loops

2017/10/06 by Xiang He, He, Xiang
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1710.02288

openalex publication_date 2017/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Proves that if a curve has totally split reduction and the corresponding skeleton (as a metric graph) is a chain of loops with generic edge lengths, then every divisor on the graph with imposed ramification at the rightmost vertex p of the skeleton lifts to a divisor class on the curve with the same ramification at some point P that retracts to p, extending the work of Cartwright-Jensen-Payne. Gives a positive answer to lifting proper tropical intersections within a polytopal domain in an analytic torus.

Citations

• A Generalization of Lifting Non-proper Tropical Intersections

Related

• Lifting tropical self intersections
• (Hurwitz-)Brill-Noether general marked graphs via the Demazure product
• Effective divisor classes on metric graphs
• Lifting Tropical Curves in Space and Linear Systems on Graphs
• Reduced Divisors and Embeddings of Tropical Curves