Combinatorial decomposition theorem for Hitchin systems via zonotopes
Mirko Mauri, Luca Migliorini, Roberto Pagaria
TL;DR
This paper establishes a combinatorial decomposition for Hitchin systems using zonotopes, providing a new geometric perspective on their structure and spectral curve analysis.
Contribution
It introduces an equivariant lattice point counting formula for graphical zonotopes to analyze Hitchin system decompositions in arbitrary degree.
Findings
Decomposition theorem for Hitchin systems over reduced spectral curves
Equivariant lattice point count formula for graphical zonotopes
New geometric approach to Hitchin system analysis
Abstract
We determine the summands of the decomposition theorem for the Hitchin system for , in arbitrary degree, over the locus of reduced spectral curves. The key ingredient is an equivariant formula for lattice point counts in graphical zonotopes.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Algebra and Geometry · Algebraic structures and combinatorial models