Related papers: Frobenius manifolds, projective special geometry a…
Manifolds with a commutative and associative multiplication on the tangent bundle are called F-manifolds if a unit field exists and the multiplication satisfies a natural integrability condition. They are studied here. They are closely…
A smooth hypersurface over a finite field $\mathbb{F}_q$ is called Frobenius nonclassical if the image of every geometric point under the $q$-th Frobenius endomorphism remains in the unique hyperplane tangent to the point. In this paper, we…
In this paper, we study bi-Hermitian metrics on complex surfaces with split holomorphic tangent bundle and construct 2 types of metric cones. We introduce a new type of fully non-linear geometric PDE on such surfaces and establish smooth…
Necessary and sufficient conditions for some deformation algebras to provide formal Frobenius structures are given. Also, examples of formal Frobenius structures with fundamental tensor that is not of the deformation type and examples of…
We prove divisorial canonicity of Fano double hypersurfaces of general position.
We apply Frobenius integrability theorem in the search of invariants for one-dimensional Hamiltonian systems with a time-dependent potential. We obtain several classes of potential functions for which Frobenius theorem assures the existence…
In this paper we study higher Gaussian (or Wahl) maps for the canonical bundle of certain smooth projective curves. More precisely, we determine the rank of higher Gaussian maps of the canonical bundle for plane curves, for curves contained…
We prove the Dubrovin's conjecture for the Stokes matrices for the quantum cohomology of orbifold projective lines. The conjecture states that the Stokes matrix of the first structure connection of the Frobenius manifold constructed from…
We investigate the connections between the differential-geometric properties of the exponential map from the space of real skew symmetric matrices onto the group of real special orthogonal matrices and the manifold of real orthogonal…
Following the approach of Carlet et al.(2011)\cite{CDM}, we construct a class of infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy, which are defined on the space of pairs of meromorphic functions with possibly…
We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e.…
We prove analogues for Cartan geometries of Gromov's major theorems on automorphisms of rigid geometric structures. The starting point is a Frobenius theorem, which says that infinitesimal automorphisms of sufficiently high order integrate…
All parabolic geometries, i.e. Cartan geometries with homogeneous model a real generalized flag manifold, admit highly interesting classes of distinguished curves. The geodesics of a projective class of connections on a manifold, conformal…
We study the structure of Frobenius splittings (and generalizations thereof) induced on compatible subvarieties $W \subseteq X$. In particular, if the compatible splitting comes from a compatible splitting of a divisor on some birational…
We construct an isomorphism of graded Frobenius algebras between the orbifold Chow ring of weighted projective spaces and graded algebras of groups of roots of the unity.
This paper provides an alternative description for the fixed points of the fractal operator associated with a mixed possibly infinite iterated function system via a canonical projection type function. Some visual aspects of our results are…
We study smooth projective varieties with small dual variety using methods from symplectic topology. We prove the affine parts of such varieties are subcritical, and that the hyperplane class is invertible in their quantum cohomology. We…
In this article we describe three constructions of complex variations of Hodge structure, proving the existence of interesting opposite filtrations that generalize a construction of Deligne. We also analyze the relation between deformations…
In the present paper we study geometric structures associated with webs of hypersurfaces. We prove that with any geodesic (n+2)-web on an n-dimensional manifold there is naturally associated a unique projective structure and, provided that…
We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals…