Year: 2026
Type: preprint
Abstract: We derive new upper bounds for the real degree of the contour of the amoeba of algebraic curves and hypersurfaces. Our approach refines the Pfaffian method of Lang--Shapiro--Shustin by replacing large total-degree estimates with logarithmic-conormal elimination and sparse mixed-volume techniques based on the transformed Newton polytopes. This yields universal bounds together with significantly sharper sparse estimates for broad classes of Laurent polynomials. Several comparisons and explicit examples illustrate the improvement of the new bounds over the previously known universal estimates.
Source: arXiv (Cornell University)
Author: Nisse, Mounir
Institution: Xiamen University Malaysia
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Xiamen University
OpenAlex ID: W7169808722
Cites:
Cited by:
Related to: