fairfolio
Saved Projects

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

ISEF · 2025 Mathematics

Kan, Frank · Oregon Episcopal School

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.

Competition history

Resources

Related projects

Closest projects by meaning, across every fair and year in the corpus.

Browse more like this

Source: Regeneron International Science and Engineering Fair

Save projects to your library

Sign in with Google to keep track of projects you find interesting, organized into folders. An account also raises your daily allowance for “Has this been done?”, and lets you create a key for the MCP server with a much higher limit than anonymous use. Browsing stays public.

Continue with Google