Weierstrass gap sequences and their weights on tropical curves
Omid Amini, Shu Kawaguchi
TL;DR
This paper studies Weierstrass gap sequences on tropical curves, analyzing their structure and connections to algebraic curves through tropicalization, advancing understanding of tropical geometry and its relation to classical algebraic geometry.
Contribution
It introduces a detailed analysis of Weierstrass gap sequences on tropical curves and explores their correspondence with algebraic curve gap sequences via tropicalization.
Findings
Structural properties of Weierstrass gap sequences on tropical curves
Relationship established between tropical and algebraic Weierstrass gap sequences
Insights into how tropicalization preserves gap sequence features
Abstract
Given a divisor on a tropical curve, we associate to each point of the curve a Weierstrass gap sequence. We investigate structural properties of these gap sequences and explore their relationship with the Weierstrass gap sequences of line bundles on algebraic curves via the tropicalization process.
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Cryptography and Residue Arithmetic