On the rational parametric solution of diagonal quartic varieties

TL;DR

This paper presents a method to find rational parametric solutions for diagonal quartic varieties using Calabi-Yau varieties, including elliptic curves and diagonal quartic surfaces.

Contribution

It introduces a novel approach leveraging Calabi-Yau varieties to solve diagonal quartic Diophantine equations parametrically.

Findings

Rational solutions for diagonal quartic varieties are constructed.

Calabi-Yau varieties are effective tools in solving these equations.

The method broadens understanding of Diophantine solutions in higher dimensions.

Abstract

In this paper we will exhibit a rational parametric solution for the Diophantine equations of diagonal quartic varieties. Our approach is based on utilizing the Calabi-Yau varieties including elliptic curves and diagonal quartic surfaces.