相关论文: Dubrovin duality for open Hurwitz flat F-manifolds

Solutions to the Riemann-Hilbert problems with irregular singularities naturally associated to semisimple Frobenius manifold structures on Hurwitz spaces (moduli spaces of meromorphic functions on Riemann surfaces) are constructed. The…

For any generalized Frobenius manifold with non-flat unity, we construct a bihamiltonian integrable hierarchy of hydrodynamic type which is an analogue of the Principal Hierarchy of a Frobenius manifold. We show that such an integrable…

For any semisimple Frobenius manifold, we prove that a tau-symmetric bihamiltonian deformation of its Principal Hierarchy admits an infinite family of linearizable Virasoro symmetries if and only if all the central invariants of the…

Consider the genus one Hurwitz space $\mathcal{H}_1(n_0,\dots,n_m)$ of ramified covering of fixed degree with $m+1$ prescribed poles of order $n_0+1,\dots,n_m+1$, respectively. Based on a recent formula proved in \cite{Rejeb23}, we derive…

We study the family of ordinary differential equations associated to a Dubrovin-Frobenius manifold along its caustic. Upon just loosing an idempotent at the caustic and under a non-degeneracy condition, we write down a normal form for this…

In the first part of this paper, we give a new analytical proof of a theorem of C. Sabbah on integrable deformations of meromorphic connections on $\mathbb P^1$ with coalescing irregular singularities of Poincar\'e rank 1, and generalizing…

The stability of prepotential derivatives for Frobenius manifolds associated with A_N and D_N singularities has been utilized to construct (2+1)-dimensional dispersionless integrable hierarchies. Although the generalization of this…

A Riemannian metric is called Hessian if, locally, it can be written as the Hessian of a function called the Hessian potential. A (flat) Manin-Frobenius manifold is a flat Riemannian manifold furnished with a commutative and associative…

This is a survey of the current state of the theory of $F$--(super)manifolds $(M,\circ)$, first defined in [HeMa] and further developed in [He], [Ma2], [Me1]. Here $\circ$ is an $\Cal{O}_M$--bilinear multiplication on the tangent sheaf…

We introduce isomonodromy Knizhnik-Zamolodchikov (KZ) connections with respect to the quantum Stokes matrices, and prove that the classical limit of the KZ type connections gives rise to the Dubrovin connections of semisimple Frobenius…

Flat structure was introduced by K. Saito and his collaborators at the end of 1970's. Independently the WDVV equation arose from the 2D topological field theory. B. Dubrovin unified these two notions as Frobenius manifold structure. In this…

F-theoretic constructions can alternatively be understood as consequences of certain N = 2 Seiberg-Witten theories via type IIB r D3s probing the quantum corrected orientifold backgrounds. We present four models that come out from such…

We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules. This is motivated by the Nakayama conjecture and an approach of Martinez-Villa to the Auslander-Reiten conjecture…

We consider a Frobenius structure associated with the dispersionless Kadomtsev-Petviashvili equation. This is done, essentially, by applying a continuous analogue of the finite dimensional theory in the space of Schwartz functions on the…

We define the concept of a flat pseudo-Riemannian $F$-Lie algebra and construct its corresponding double extension. This algebraic structure can be interpreted as the infinitesimal analogue of a Frobenius Lie group devoid of Euler vector…

In a recent paper [8], it is proved that the genus two free energy of an arbitrary semisimple Frobenius manifold can be represented as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus…

A Frobenius manifold is a manifold with a flat metric and a Frobenius algebra structure on tangent spaces at points of the manifold such that the structure constants of multiplication are given by third derivatives of a potential function…

In this paper we study $F$-manifolds equipped with multiple flat connections (and multiple $F$-products), that are required to be compatible in a suitable sense. In the semisimple case we show that a necessary condition for the existence of…

We give a conjugacy relation on certain type of Frobenius manifold structures using the theory of flat pencils of metrics. It leads to a geometric interpretation for the inversion symmetry of solutions to Witten-Dijkgraaf-Verlinde-Verlinde…

Generalizing a construction presented in [3], we show that the orbit space of $B_2$ less the image of coordinate lines under the quotient map is equipped with two Dubrovin-Frobenius manifold structures which are related respectively to the…