Related papers: On the Frobenius Manifolds for Cusp Singularities

We construct a class of infinite-dimensional Frobenius manifolds on the space of pairs of certain even functions meromorphic inside or outside the unit circle. Via a bi-Hamiltonian recursion relation, the principal hierarchies associated to…

An $F$-manifold is complex manifold with a multiplication on the holomorphic tangent bundle with a certain integrability condition. Important examples are Frobenius manifolds and especially base spaces of universal unfoldings of isolated…

We obtain polynomial Frobenius manifolds from classical $W$-algebras associated to regular nilpotent elements in simple Lie algebras using the related opposite Cartan subalgebras.

The base space of a semiuniversal unfolding of a hypersurface singularity carries a rich geometry. By work of K. Saito and M. Saito is can be equipped with the structure of a Frobenius manifold. By work of Cecotti and Vafa it can be…

We consider a holomorphic 1-form $\omega$ with an isolated zero on an isolated complete intersection singularity $(V,0)$. We construct quadratic forms on an algebra of functions and on a module of differential forms associated to the pair…

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…

Starting from a cubic form, we give a general construction of a quasi-complete homogeneous manifold endowed with a natural contact structure. We show that it can be compactified into a projective contact manifold if and only if the cubic…

We prove that the Chow motives of two smooth cubic fourfolds whose Kuznetsov components are Fourier-Mukai derived-equivalent are isomorphic as Frobenius algebra objects. As a corollary, we obtain that there exists a Galois-equivariant…

In a recent paper Garoufalidis and Reid constructed pairs of 1-cusped hyperbolic 3-manifolds which are isospectral but not isometric. In this paper we extend this work to the multi-cusped setting by constructing isospectral but not…

We present an approach to construct a class of generalized Frobenius manifold structures on the orbit spaces of affine Weyl groups, and prove that their monodromy groups are parabolic subgroups of the associated affine Weyl groups.

Combining geometric group theory techniques with geometric topology tools, we show how primitive cohomologies provide useful insights towards unifying the mathematical formulation of Gromov-Witten invariants. In particular, we emphasise the…

This paper studies graded manifolds with local coordinates concentrated in non-negative degrees. We provide a canonical description of these objects in terms of classical geometric data and, building on this geometric viewpoint, we prove…

We prove that in any strictly convex symmetric cone $\Omega$ there exists a non empty locus where the WDVV equation is satisfied (i.e. there exists a hyperplane being a Frobenius manifold). This result holds over any real division algebra…

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…

A smooth cuboid can be identified with a $3\times 3$ matrix of linear forms, with coefficients in a field $K$, whose determinant describes a smooth cubic in the projective plane. To each such matrix one can associate a group scheme over…

We provide a new $L^2$-Hodge theoretic construction of a Frobenius manifold structure on the cohomology of a Calabi-Yau smooth projective hypersurface $V$, using Li-Wen's $L^2$-Hodge theory [9] of a Landau-Ginzburg model with compact…

We study linearizability of actions of finite groups on singular cubic threefolds, using cohomological tools, intermediate Jacobians, Burnside invariants, and the equivariant Minimal Model Program.

In [19] we studied a Fadell-Neuwirth type fibration theorem for orbifolds, and gave a short exact sequence of fundamental groups of configuration Lie groupoids of Lie groupoids corresponding to the genus zero 2-dimensional orbifolds with…

The orbits space of an irreducible linear representation of a finite group is a variety whose coordinate ring is the ring of invariant polynomials. Boris Dubrovin proved that the orbits space of the standard reflection representation of an…

Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux-Egoroff equations. This system of partial differential equations appears as a specific subset of the $n$-component KP…