Bethe Subspaces and Toric Arrangements
Mathematics#Algebraic Geometry, Integrable Systems🔬 Research|Analyzed: Jan 3, 2026 18:45•
Published: Dec 29, 2025 14:02
•1 min read
•ArXivAnalysis
This paper explores the geometry of Bethe subspaces, which are related to integrable systems and Yangians, and their connection to toric arrangements. It provides a compactification of the parameter space for these subspaces and establishes a link to the logarithmic tangent bundle of a specific geometric object. The work extends and refines existing results in the field, particularly for classical root systems, and offers conjectures for future research directions.
Key Takeaways
- •Introduces and studies Bethe subspaces within the context of trigonometric holonomy Lie algebras.
- •Provides a compactification of the parameter space for Bethe subspaces using the minimal wonderful model of a toric arrangement.
- •Establishes connections between Bethe subspaces and the logarithmic tangent bundle.
- •Refines existing results and offers conjectures for future research, particularly in the context of Yangians and quantum cohomology.
Reference / Citation
View Original"The paper proves that the family of Bethe subspaces extends regularly to the minimal wonderful model of the toric arrangement."