Transfinite diameter on the graph of a polynomial mapping and the DeMarco–Rumely formula

Abstract

We study Chebyshev constants and transfinite diameter on the graph of a polynomial mapping f:{{mathbb {C}}}^2rightarrow {{mathbb {C}}}^2. We show that two transfinite diameters of a compact subset of the graph (i.e., defined with respect to two different collections of monomials) are equal when the set has a certain symmetry. As a consequence, we give a new proof in {{mathbb {C}}}^2 of a pullback formula for transfinite diameter due to DeMarco and Rumely that involves a homogeneous resultant.