Chebyshev constants, transfinite diameter, and computation on complex algebraic curves

TL;DR

This paper extends the concepts of Chebyshev constants and transfinite diameter from algebraic curves in two complex dimensions to higher dimensions, utilizing advanced computational algebraic geometry techniques.

Contribution

It generalizes existing theories to complex algebraic curves in any dimension, enhancing computational methods for these geometric invariants.

Findings

Extended Chebyshev constants and transfinite diameter to $ ext{C}^N$

Developed new computational algebraic geometry methods

Established analogous properties in higher dimensions

Abstract

Notions of directional Chebyshev constant and transfinite diameter have recently been studied on certain algebraic curves in $\mathbb{C}^2$. The theory is extended here to curves in $\mathbb{C}^N$ for arbitrary $N$. The results are analogous but require more methods from computational algebraic geometry.