Elementary Moves on Ideal Webs, Local Monodromies on Hitchin Fibrations, and Tropical Mutations on K₀ Groups

@misc{liao2026elementary,
  title = {{Elementary Moves on Ideal Webs, Local Monodromies on Hitchin Fibrations, and Tropical Mutations on $\mathrmK_0$ Groups}},
  author = {Yuhan Liao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35898},
  eprint = {2610.35898},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35898},
}

TY  - UNPB
TI  - Elementary Moves on Ideal Webs, Local Monodromies on Hitchin Fibrations, and Tropical Mutations on K_0 Groups
AU  - Yuhan Liao
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.35898
UR  - https://arxiv.org/abs/2610.35898
AB  - This paper builds on the work of Goncharov by studying the correspondence between topological spectral covers constructed from generic A_m−1-webs with rank m≥2, Hitchin spectral curves over good Hitchin loci, and the Grothendieck groups K_0(𝒟_Γ) associated with the quivers with potential (Q_Γ,W_Γ) assigned to corresponding bipartite A_m−1-graphs. We show that the automorphisms on the non-frozen quiver lattices Λ_Γ^∘ induced by compositions of elementary moves on ideal webs/bipartite graphs are the same as the Gauss--Manin monodromy actions on the SL_m Hitchin fiber lattices H_1(Prym(Σ);ℤ) locally around discriminant loci. And the Gauss--Manin monodromy actions agree with the automorphisms on the Grothendieck groups K_0(𝒟_Γ^∘) induced by compositions of mutations on the quivers with potential (Q_Γ,W_Γ).
ER  -