Related papers: On the Frobenius integrability of certain holomorp…
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 address the problem of classification of contact Fano manifolds. It is conjectured that every such manifold is necessarily homogeneous. We prove that the Killing form, the Lie algebra grading and parts of the Lie bracket can be read from…
In this paper we describe the action of the Frobenius morphism on the indecomposable vector bundles on cycles of projective lines. This gives an answer on a question of Paul Monsky, which appeared in his study of the Hilbert--Kunz theory…
A recent celebrated theorem of Diverio-Trapani and Wu-Yau states that a compact K\"ahler manifold admitting a K\"ahler metric of quasi-negative holomorphic sectional curvature has an ample canonical line bundle, confirming a conjecture of…
The notion of a Frobenius manifold appears in relation to various topics in algebraic and analytic geometry, such and quantum cohomology, deformation of meromorphic connections, unfolding of singularities and others. In the local setting…
Submanifolds of Frobenius manifolds are studied. In particular, so-called natural submanifolds are defined and, for semi-simple Frobenius manifolds, classified. These carry the structure of a Frobenius algebra on each tangent space, but…
We generalize, explain and simplify Langer's results concerning Frobenius direct images of line bundles on quadrics, describing explicitly the decompositions of higher Frobenius push-forwards of arithmetically Cohen-Macaulay bundles into…
We formulate the non-commutative integrability of contact systems on a contact manifold $(M,\mathcal H)$ using the Jacobi structure on the space of sections $\Gamma(L)$ of a contact line bundle $L$. In the cooriented case, if the line…
Let X be a compact connected Kaehler manifold such that the holomorphic tangent bundle TX is numerically effective. A theorem of Demailly, Peternell and Schenider says that there is a finite unramified Galois covering M --> X, a complex…
Quantum homogeneous vector bundles are introduced by a direct description of their sections in the context of Woronowicz type compact quantum groups. The bundles carry natural topologies inherited from the quantum groups, and their sections…
We provide supplements and open problems related to structure theorems for maximal rationally connected fibrations of certain positively curved projective varieties, including smooth projective varieties with semi-positive holomorphic…
Consider a meromorphic connection on P^1 over a p-adic field. In many cases, such as those arising from Picard-Fuchs equations or Gauss-Manin connections, this connection admits a Frobenius structure defined over a suitable rigid analytic…
Consider a very ample line bundle $ E \to X$ over a compact complex manifold, endowed with a hermitian metric of curvature $-i \omega $, and the space $\mathcal{O}(E)$ of its holomorphic sections. The Fubini--Study map associates with…
This paper is based on the author's talk at 1997 Taniguchi Symposium ``Integrable Systems and Algebraic Geometry''. We consider an approach to the theory of Frobenius manifolds based on the geometry of flat pencils of contravariant metrics.…
This paper stresses the strong link between the existence of partial holomorphic connections on the normal bundle of a foliation seen as a quotient of the ambient tangent bundle and the extendability of a foliation to an infinitesimal…
We prove there is a class of maps $\gamma:\mathbb{T}^{2n}\rightarrow\mathbb{S}^1$ such that a conservative dynamically coherent partially hyperbolic skew-product on $\mathbb{T}^{2n}\times\mathbb{S}^1$ with fixed hyperbolic dynamics on the…
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…
The goal of this survey is to present various results concerning the cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and related properties of their multiplier ideal sheaves. In case the curvature is strictly…
This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and…
We establish a stable homotopy-theoretic version of a recent result of Farber and Weinberger on the fibrewise topological complexity of sphere bundles and prove, by closely parallel methods, a similar result for real, complex and…