# A correction to the paper "On Curves with Split Jacobian"

## TL;DR

This paper corrects and clarifies the genus formula for a family of algebraic curves, providing an algebraic proof and identifying conditions under which the original formula is valid.

## Contribution

It offers a corrected genus formula with an algebraic proof and specifies the conditions for its valid application, improving upon prior incomplete results.

## Key findings

- Corrected genus formula for certain algebraic curves
- Algebraic proof of the genus formula
- Conditions under which the original formula applies

## Abstract

In [5], without giving a detailed proof, Yamauchi provided a formula to calculate the genus of a certain family of smooth complete intersection algebraic curves. That formula is used extensively in [1] to study the algebraic curves for which their Jacobian has superelliptic components. In this note, we determine the correct version of the genus formula with an algebraic proof. Then, we show that the formula given in [5] works only under certain conditions.