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Combinatorial Invaraints of Stable Curve in Genus 4: Classification and Computation

ISEF · 2025 Mathematics

Kan, Frank · Oregon Episcopal School

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Overview

This study delves into the computation and classification of combinatorial invariants associated with stable curves in genus 4. The work builds upon Zhang's decomposition formula, emphasizing local contributions from non-Archimedean places. By classifying dual graphs and developing algorithms for the explicit computation of admissible invariants like epsilon(gamma), phi(gamma), and lambda(gamma), this paper extends prior results for genus 3 curves. The methodologies and algorithms provided have broader applicability, which offers potential insights into higher-genus curves and connections between arithmetic geometry and physics.

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Source: Regeneron International Science and Engineering Fair

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