Geometry of generalized amoebas
Yury Eliyashev
TL;DR
This paper extends the concept of amoebas and Ronkin functions from plane algebraic curves to higher dimensions, translating key geometric properties to this generalized setting.
Contribution
It introduces a higher-dimensional generalization of amoebas and adapts known geometric results to this new context.
Findings
Higher-dimensional amoebas are characterized and studied.
Geometric properties of amoebas are extended to the generalized case.
The work provides a foundation for further exploration of higher-dimensional amoebas.
Abstract
Recently Krichever proposed a generalization of the amoeba and the Ronkin function of a plane algebraic curve. In our paper higher-dimensional version of this generalization is studied. We translate to the generalized case different geometric results known in the standard amoebas case.
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Topological and Geometric Data Analysis