Transfinite diameter on the graph of a polynomial mapping and the DeMarco-Rumely formula
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866913342874976256 |
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| author | Ma`u, Sione |
| author_facet | Ma`u, Sione |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2111_08368 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Transfinite diameter on the graph of a polynomial mapping and the DeMarco-Rumely formula Ma`u, Sione Complex Variables 32U20 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. |
| title | Transfinite diameter on the graph of a polynomial mapping and the DeMarco-Rumely formula |
| topic | Complex Variables 32U20 |
| url | https://arxiv.org/abs/2111.08368 |