Related papers: Holomorphic Engel Structures
Call a pure Hodge structure geometric if it is contained in the cohomology of a smooth complex projective variety. The main goal is to show that for any set of Hodge numbers (subject to the obvious constraints), there exists a geometric…
In this article, we treat G_2-geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G_2-structure; in…
Johnson and Livingston have characterized peripheral structures in homomorphs of knot groups. We extend their approach to the case of links. The main result is an algebraic characterization of all possible peripheral structures in certain…
This article is devoted to investigations of a structure and homomorphisms of microbundles. Microbundles are generalizations of manifolds. For manifolds it was studied when their families of homomorphism can be supplied with the manifold…
We study ergodic properties of compositions of holomorphic endomorphisms of the complex projective space chosen independently at random according to some probability distribution. Along the way, we construct positive closed currents which…
Every algebraic variety can be regarded as a symplectic manifold being equipped with a Kahler form. Therefore it is natural to study lagrangian geometry of any algebraic variety. We present two basic constructions which can be applied to a…
In this paper, we introduce homological structure theory of semirings and CP-semirings---semirings all of whose cyclic semimodules are projective. We completely describe semisimple, Gelfand, subtractive, and anti-bounded, CP-semirings. We…
We introduce a natural notion of holomorphic map between generalized complex manifolds and we prove some related results on Dirac structures and generalized Kaehler manifolds.
We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine…
We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…
We give a new proof of the classification of normal singular surface germs admitting non-invertible holomorphic self-maps and due to J. Wahl. We then draw an analogy between the birational classification of singular holomorphic foliations…
We study the problem of classifying local projective structures in dimension two having non trivial Lie symmetries. In particular we obtain a classification of flat projective structures having positive dimensional Lie algebra of projective…
The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical…
This is a survey on quaternion Hermitian Weyl (locally conformally quaternion K\"ahler) and hyperhermitian Weyl (locally conformally hyperk\"ahler) manifolds. These geometries appear by requesting the compatibility of some quaternion…
The complex projective structures considered is this article are compact curves locally modeled on $\mathbb{CP}^1$. To such a geometric object, modulo marked isomorphism, the monodromy map associates an algebraic one: a representation of…
We provide a simple construction of bipartite entangled states that are positive under partial transposition, and hence undistillable. The construction makes use of the properties of the projectors onto the symmetric and antisymmetric…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
Etale endomorphisms of complex projective manifolds are constructed from two building blocks up to isomorphism if the good minimal model conjecture is true. They are the endomorphisms of abelian varieties and the nearly etale rational…
The main aim of this paper is to classify the distinct multiplicative Lie algebra structures (up to isomorphism) on a given group. We also see that for a given group $G$, every homomorphism from the non-abelian exterior square $G \wedge G$…
We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for…