arXiv subjects

Alessandro Proserpio

Publications and source records attributed to Alessandro Proserpio.

4 recordsLinked to original sources

arXiv2026

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

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.

math-ph↗

arXiv2026

Open WDVV equations and $\bigvee$-systems

The idea of a $\bigvee$-system was introduced by Veselov in the study of rational solutions of the WDVV equations of associativity. These are algebraic/geometric conditions on the set of covectors that appear in rational solutions to the WDVV equations. Here, this idea is generalized to open WDVV equations, which are an additional set of PDEs originating from open Gromow-Witten Theory. We develop -- for rank-one extensions -- algebraic/geometric conditions on the covectors that supplement the $\bigvee$-system to give rational solutions to the open WDVV equations. Examples, and the relation to superpotentials and to Dubrovin almost-duality, are given.

math-ph↗

arXiv2025

Dubrovin duality for open Hurwitz flat F-manifolds

We prove that the Dubrovin dual of a Hurwitz Frobenius manifold extends naturally to an F-manifold with compatible flat connection on the universal curve, in the sense of the open WDVV equations. A similar result is proven for the Frobenius manifold itself in arXiv:2503.09258 . This equips the universal curve with two F-manifolds with compatible flat structure, and we study their duality. We show that they combine into a bi-flat F-manifold. Conditions on open WDVV solutions imposed in previous work are retrieved in this setting, thus providing them with a geometrical meaning. Finally, explicit examples are computed. For Saito Frobenius manifolds of types $A$ and $D$, the extended prepotentials coincide with open WDVV solutions computed independently, whereas even the existence of the solution in type $E$ had not been previously discussed. On the other hand, new non-homogeneous solutions are constructed by duality.

math-ph↗

arXiv2024

Diagonal invariants and genus-zero Hurwitz Frobenius manifolds

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 $W=W(A_\ell)\,.$ An invariant theory is also developed.

math-ph↗