2018/02/13 by Jesse Hart, Hart, Jesse
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #math.AG #math.CV
paper · pdf · doi:10.48550/arxiv.1802.04430
17 pages
arxiv created 2018/02/13 · openalex publication_date 2018/02/13 · arxiv updated 2018/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a compact set K one may define a transfinite diameter for K via a limiting process involving maximising a Vandermonde determinant over K with respect to a monomial basis. Different transfinite diameters may be obtained by using different polynomial bases in the Vandermonde determinant calculation. We show that if these bases are sufficiently similar that the transfinite diameter of K is unchanged. Utilising this result we show that the transfinite diameters defined by Cox-Ma`u and Berman-Boucksom for algebraic varieties are equal.