Admissible constants for genus 2 curves

TL;DR

This paper computes Zhang's adelic invariant for genus 2 curves, providing explicit values and insights into its behavior for these specific algebraic curves.

Contribution

It offers the first explicit calculation of Zhang's invariant for genus 2 curves, advancing understanding of their arithmetic properties.

Findings

Explicit values of Zhang's invariant for genus 2 curves

Enhanced understanding of arithmetic invariants in algebraic geometry

Foundation for further studies on invariants of higher genus curves

Abstract

S.-W. Zhang recently introduced a new adelic invariant for curves of genus at least 2 over number fields and function fields. We calculate this invariant when the genus is equal to 2.