3 papers
math.AG2026
Tropical Weierstrass points and Weierstrass weights
Omid Amini, Lucas Gierczak, Harry Richman
In this paper, we study tropical Weierstrass points. These are the analogues for tropical curves of ramification points of line bundles on algebraic curves. For a divisor on a trop…
math.AG2026
Equality of tropical rank and dimension for semimodules of tropical rational functions, and computational aspects
Omid Amini, Stéphane Gaubert, Lucas Gierczak
The tropical rank of a semimodule of rational functions on a metric graph mirrors the concept of rank in linear algebra. Defined in terms of the maximal number of tropically indepe…
math.AG2024
Limit linear series: combinatorial theory
Omid Amini, Lucas Gierczak
We develop a purely combinatorial theory of limit linear series on metric graphs. This will be based on the formalisms of hypercube rank functions and slope structures. We provide…