Combinatorial decomposition theorem for Hitchin systems via zonotopes
Algebraic Geometry
2023-07-07 v2 Combinatorics
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.
Cite
@article{arxiv.2209.00621,
title = {Combinatorial decomposition theorem for Hitchin systems via zonotopes},
author = {Mirko Mauri and Luca Migliorini and Roberto Pagaria},
journal= {arXiv preprint arXiv:2209.00621},
year = {2023}
}
Comments
49 pages. 7 figures. 2 tables. We strengthen the results of the first version and solve open problems in there: we can now provide a complete description of the decomposition theorem for the Hitchin system on the locus of reduced spectral curves