Identities for hyperelliptic P-functions of genus one, two and three in covariant form

TL;DR

This paper provides a covariant framework for quadratic differential identities of P-functions on Jacobians of hyperelliptic curves with genus 1, 2, and 3, enhancing understanding of their algebraic structure.

Contribution

It introduces a covariant approach to quadratic identities of P-functions for hyperelliptic curves of low genus, extending previous non-covariant formulations.

Findings

Covariant form of quadratic identities for genus 1, 2, and 3 hyperelliptic P-functions

Unified treatment across multiple genera

Enhanced algebraic understanding of P-functions on Jacobians

Abstract

We give a covariant treatment of the quadratic differential identities satisfied by the P-functions on the Jacobian of smooth hyperelliptic curves of genera 1, 2 and 3.