Canonical Height Functions For Monomial Maps
Jan-Li Lin, Chi-Hao Wang
TL;DR
This paper introduces a new canonical height function for monomial maps that overcomes limitations of Silverman's original function, providing better properties in specific cases.
Contribution
Develops a novel canonical height function for monomial maps that improves upon Silverman's in certain scenarios.
Findings
Silverman's canonical height lacks Northcott finiteness in general
New canonical height function has desirable properties in specific cases
Enhances understanding of height functions for monomial maps
Abstract
We show that the canonical height function defined by Silverman does not have the Northcott finiteness property in general. We develop a new canonical height function for monomial maps. In certain cases, this new canonical height function has nice properties.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry