Diagonal invariants and genus-zero Hurwitz Frobenius manifolds
Mathematical Physics
2026-01-08 v2 math.MP
Exactly Solvable and Integrable Systems
Abstract
The Frobenius manifold structure on the space of rational functions with multiple simple poles is constructed. In particular, the dependence of the Saito-flat coordinates on the flat coordinates of the intersection form is studied. While some of the individual flat coordinates are complicated rational functions, they appear in the prepotential in certain combinations known as diagonal invariants, which turn out to be polynomial. Two classes are studied in more detail. These are generalisations of the Coxeter and extended-affine-Weyl orbits space for the group An invariant theory is also developed.
Cite
@article{arxiv.2412.05165,
title = {Diagonal invariants and genus-zero Hurwitz Frobenius manifolds},
author = {Alessandro Proserpio and Ian A. B. Strachan},
journal= {arXiv preprint arXiv:2412.05165},
year = {2026}
}
Comments
Final version, accepted for publication on Selecta Math