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arXiv · 2609.10019

The Elusive Relatively K-Unstable Delzant Octagon: A Numerical Search

Thibaut Delcroix·Bijan Mohammadi
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Abstract

Relative K-stability of toric varieties can be tested through explicit Donaldson-Futaki computations, yet finding unstable examples remains challenging. We develop a reproducible symbolic-numeric framework to investigate all fifteen families of Delzant octagons corresponding to smooth toric surfaces of Picard rank six. While numerical optimization identifies several apparently destabilizing configurations, exact rational reconstruction systematically removes the observed instability. We explain why Wang and Zhou's 2014 tentative construction of a relatively K-unstable octagon does not allow to find an explicit example.

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Thibaut Delcroix, Bijan Mohammadi. 2026-09-09. The Elusive Relatively K-Unstable Delzant Octagon: A Numerical Search. https://arxiv.org/abs/2609.10019

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