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arXiv · 2111.08368

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

Sione Ma`u
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Abstract

We study Chebyshev constants and transfinite diameter on the graph of a polynomial mapping $f\colon\mathbb{C}^2\to\mathbb{C}^2$. 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.

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Sione Ma`u. 2021-11-16. Transfinite diameter on the graph of a polynomial mapping and the DeMarco-Rumely formula. https://doi.org/10.1007/s40879-022-00555-3

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