Limit linear series: combinatorial theory
Omid Amini, Lucas Gierczak
TL;DR
This paper develops a combinatorial framework for limit linear series on metric graphs, utilizing hypercube rank functions and slope structures, and classifies rank one series with connections to tropical and combinatorial algebraic geometry.
Contribution
It introduces a new combinatorial approach to limit linear series on metric graphs, including a full classification for rank one cases.
Findings
Classified all rank one combinatorial limit linear series.
Established connections to tropical algebra.
Provided formalism based on hypercube rank functions and slope structures.
Abstract
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 a full classification of combinatorial limit linear series of rank one, and discuss connections to other concepts in tropical algebra and combinatorial algebraic geometry.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Polynomial and algebraic computation · Data Management and Algorithms