Landau-Ginzburg models of generalised Dubrovin-Zhang form and pole collision: Dynkin-type A

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Main Authors: Proserpio, Alessandro, van Gemst, Karoline
Format: Preprint
Published: 2026
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author Proserpio, Alessandro
van Gemst, Karoline
author_facet Proserpio, Alessandro
van Gemst, Karoline
contents In arXiv:1711.05958, arXiv:2103.12673, the authors derive one-dimensional Landau-Ginzburg mirrors of Dubrovin-Zhang Frobenius manifolds constructed on regular orbit spaces of an extension of affine Weyl groups. We generalise the method employed, and classify the resulting Frobenius manifold structures in Dynkin type A. We interpret our results in terms of a stratification on the Hurwitz space boundary, and develop a pole-collision framework to compare the Frobenius structures within different strata. With this, we can prove a structural result at the level of the prepotential, for arbitrary rank and dimension, as a suitable renormalised limit of the formulae in arXiv:2412.05165. As a corollary, a conjecture of Ma and Zuo regarding the form of prepotentials related to doubly-extended affine Weyl groups is proven.
format Preprint
id arxiv_https___arxiv_org_abs_2605_21749
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Landau-Ginzburg models of generalised Dubrovin-Zhang form and pole collision: Dynkin-type A
Proserpio, Alessandro
van Gemst, Karoline
Mathematical Physics
Algebraic Geometry
Differential Geometry
Exactly Solvable and Integrable Systems
53D45 (Primary) 14H70, 37K10 (Secondary)
In arXiv:1711.05958, arXiv:2103.12673, the authors derive one-dimensional Landau-Ginzburg mirrors of Dubrovin-Zhang Frobenius manifolds constructed on regular orbit spaces of an extension of affine Weyl groups. We generalise the method employed, and classify the resulting Frobenius manifold structures in Dynkin type A. We interpret our results in terms of a stratification on the Hurwitz space boundary, and develop a pole-collision framework to compare the Frobenius structures within different strata. With this, we can prove a structural result at the level of the prepotential, for arbitrary rank and dimension, as a suitable renormalised limit of the formulae in arXiv:2412.05165. As a corollary, a conjecture of Ma and Zuo regarding the form of prepotentials related to doubly-extended affine Weyl groups is proven.
title Landau-Ginzburg models of generalised Dubrovin-Zhang form and pole collision: Dynkin-type A
topic Mathematical Physics
Algebraic Geometry
Differential Geometry
Exactly Solvable and Integrable Systems
53D45 (Primary) 14H70, 37K10 (Secondary)
url https://arxiv.org/abs/2605.21749