Transfinite diameter on complex algebraic varieties

TL;DR

This paper extends the concept of transfinite diameter to complex algebraic varieties using computational algebraic geometry, generalizing existing formulas to higher dimensions.

Contribution

It provides a new generalization of Zaharjuta's integral formula for the Fekete-Leja transfinite diameter on algebraic varieties.

Findings

Generalized Zaharjuta's integral formula for varieties

Connected transfinite diameter with algebraic geometry methods

Enhanced understanding of Chebyshev constants on varieties

Abstract

We use methods from computational algebraic geometry to study Chebyshev constants and the transfinite diameter of a pure $m$-dimensional affine algebraic variety in $\mathbb{C}^n$ ($m\leq n$). The main result is a generalization of Zaharjuta's integral formula for the Fekete-Leja transfinite diameter.