相关论文: Embeddings of Complex Supermanifolds

This article is a continuation of a previous article which concerned the splitting problem for subspaces of superspaces. We begin with a general account of projective superspaces. Subsequently, we specialise to subvarieties of `positive'…

This is the sequel to our first paper concerning the balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. We prove the uniqueness of such an embedding. The proof relies on fine estimates of the…

For an orbifold, there is a notion of an orbifold embedding, which is more general than the one of sub-orbifolds. We develop several properties of orbifold embeddings. In the case of translation groupoids, we show that such a notion is…

The analysis of manifold valued data using embedding based methods is linked to the problem of finding suitable embeddings. In this paper we are interested in embeddings of quotient manifolds $\mathrm{SO}(3)/\mathcal{S}$ of the rotation…

Let N a compact complex submanifold of a compact complex manifold M. We say N splits in M, if the holomorphic tangent bundle sequence splits holomorphically. By a result of Mok a splitting submanifold of a Kaehler Einstein manifold with a…

In this article we study the notion of supermanifolds families, starting from Green's general classification of supermanifolds. The topics studied divide this article into two distinct parts, labelled I and II respectively. Part I concerns…

We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of…

A large class of supersymmetric extended objects is considered from the viewpoint of embeddings of super worldsurfaces into target superspaces. It is shown that a simple geometrical condition leads to the equations of motion for the brane…

We explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the exploration of the ensemble of networks which share common…

In this paper we study further when tangles embed into the unknot, the unlink or a split link. In particular, we study obstructions to these properties through geometric characterizations, tangle sums and colorings. As an application we…

1) In 1976, looking at simple finite-dimensional complex Lie superalgebras, J.~Bernstein and I, and independently M.~Duflo, observed that certain divergence-free vectorial Lie superalgebras have deformations with odd parameters and…

In this article we introduce the notion of a 'good model' in order to study the higher obstructions of complex supermanifolds. We identify necessary and sufficient conditions for such models to exist. Illustrations over Riemann surfaces are…

In this paper we give a brief account of the relations between non-projected supermanifolds and projectivity in supergeometry. Following the general results of arXiv:1706.01354, we study an explicit example of non-projected and…

Any non-split complex supermanifold is a deformation of a split supermanifold. These deformations are classified by group orbits in a non-abelian cohomology. For the case of a split supermanifold with no global nilpotent even vector fields,…

It is a classical result that any complex analytic Lie supergroup $\mathcal{G}$ is split \cite{kosz}, that is its structure sheaf is isomorphic to the structure sheaf of a certain vector bundle. However, there do exist non-split complex…

These are notes on the theory of supermanifolds and integration on them, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.

We study the spaces of embeddings of manifolds in a Euclidean space. More precisely we look at the homotopy fiber of the inclusion of these spaces to the spaces of immersions. As a main result we express the rational homotopy type of…

The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…

We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.

We consider the following question: When does a Riemannian manifold admit an embedding with a uniformly thick tubular neighborhood in another Riemannian manifold of large dimension?