Convergent Hahn Series and Tropical Geometry of Higher Rank
Michael Joswig, Ben Smith
TL;DR
This paper explores the tropical geometry derived from convergent Hahn series in multiple variables, offering new insights into stable intersections of tropical hypersurfaces and perturbations of rank one tropical polytopes for improved algorithms.
Contribution
It introduces a novel approach to tropical geometry using convergent Hahn series, enhancing understanding of stable intersections and perturbations in tropical polytopes.
Findings
New perspective on stable intersections of tropical hypersurfaces
Perturbation techniques for rank one tropical polytopes
Potential improvements in tropical algorithm efficiency
Abstract
We propose to study the tropical geometry specifically arising from convergent Hahn series in multiple indeterminates. One application is a new view on stable intersections of tropical hypersurfaces. Another one is perturbations of rank one tropical polytopes, which is beneficial for algorithmic purposes.
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Taxonomy
TopicsPolynomial and algebraic computation · Commutative Algebra and Its Applications · Cancer Treatment and Pharmacology