Transfinite diameter on complex algebraic varieties

David A. Cox and Sione Ma‘u

Vol. 291 (2017), No. 2, 279–317

DOI: 10.2140/pjm.2017.291.279

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 ${ℂ}^n$ ($m\le n$). The main result is a generalization of Zaharyuta’s integral formula for the Fekete–Leja transfinite diameter.

Keywords

Chebyshev constant, transfinite diameter, Vandermonde determinant, affine variety, Noether normalization, monomial order

Mathematical Subject Classification 2010

Primary: 32U20

Secondary: 14Q15

Milestones

Received: 16 March 2016

Revised: 11 February 2017

Accepted: 2 May 2017

Published: 14 September 2017