Related papers: On the partial algebraicity of holomorphic mapping…

We establish results on holomorphic extension of CR-mappings of class $C^\infty$ between a real-analytic CR-submanifold of $\C^N$ and a real-algebraic CR-submanifold of $\C^{N'}$.

A classical theorem of Micallef says that if $F \colon (\Sigma, g) \to \mathbb{R}^4$ is a stable minimal immersion of an oriented $2$-dimensional complete Riemannian manifold (that is parabolic) into $\mathbb{R}^4$, it is necessarily…

Given a finitely generated module $M$ over a commutative local ring (or a standard graded $k$-algebra) $(R,\m,k) $ we detect its complexity in terms of numerical invariants coming from suitable $\m$-stable filtrations $\mathbb{M}$ on $M$.…

We study non-degenerate CR geometries of hypersurface type that are symmetric in the sense that, at each point, there is a CR transformation reversing the CR distribution at that point. We show that such geometries are either flat or…

The most impressively prolific exploration of superstring models (aiming for our physical reality) has been focused on worldsheet-supersymmetric gauged linear sigma models and the closely associated complex-algebraic toric geometry. Mirror…

We give a necessary and sufficient condition for the existence of nondegenerate holomorphic mappings between pseudoellipsoidal real hypersurfaces, and provide an explicit parametrization for the collection of all such mappings (in the…

In 1974, Federer proved that all area-minimizing hypersurfaces on orientable manifolds were calibrated by weakly closed differential forms. However, in this manuscript, we prove the contrary in higher codimensions: calibrated…

We use techniques from both real and complex algebraic geometry to study K-theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, we prove a…

Let $\Omega \subset {\mathbb C}^n \times {\mathbb R}$ be a bounded domain with smooth boundary such that $\partial \Omega$ has only nondegenerate elliptic CR singularities, and let $f \colon \partial \Omega \to {\mathbb C}$ be a smooth…

The aim of the paper is to prove that if $M$ is a metrizable manifold modelled on a Hilbert space of dimension $\alpha \geq \aleph_0$ and $F$ is its $\sigma$-$Z$-set, then for every completely metrizable space $X$ of weight no greater than…

In this paper we continue our study of local rigidity for maps of CR submanifolds of the complex space. We provide a linear sufficient condition for local rigidity of finitely nondegenerate maps between minimal CR manifolds. Furthermore, we…

We prove that the characteristic foliation $F$ on a non-singular divisor $D$ in an irreducible projective hyperkaehler manifold $X$ cannot be algebraic, unless the leaves of $F$ are rational curves or $X$ is a surface. More generally, we…

We prove here new results about transversality and related geometric properties of a holomorphic, formal, or CR mapping, sending one generic submanifold of $\bC^N$ into another. One of our main results is that a finite mapping is…

A unimodular complex surface is a complex 2-manifold X endowed with a holomorphic volume form. A strictly pseudoconvex real hypersurface M in X inherits not only a CR-structure but a canonical coframing as well. In this article, this…

Let $M$ be a real $l$-dimensional minimal submanifold with flat normal connection in a kaehler product manifold $\overline{M}^m\times \overline{M}^n$ where $\overline{M}^m$ and $\overline{M}^n$ are complex $m$-dimensional and complex…

We consider minimal maps $f:M\to N$ between Riemannian manifolds $(M,\mathrm{g}_M)$ and $(N,\mathrm{g}_N)$, where $M$ is compact and where the sectional curvatures satisfy $\sec_N\le \sigma\le \sec_M$ for some $\sigma>0$. Under certain…

The purpose of this article is to show a second main theorem with the explicit truncation level for holomorphic mappings of $ \mathbb{C} $ (or of a compact Riemann surface) into a compact complex manifold sharing divisors in subgeneral…

This is the fourth of a series of papers studying real algebraic threefolds, but the methods are mostly independent from the previous ones. Let $f:X\to C$ be a map of a smooth projective real algebraic 3-fold to a curve $C$ whose general…

The model 4-dimensional CR-cubic in $\CC{3}$ has the following "model" property: it is (essentially) the unique locally homogeneous 4-dimensional CR-manifold in $\CC{3}$ with finite-dimensional infinitesimal automorphism algebra…

In this paper, we establish a general second main theorem for meromorphic mappings from $\mathbb C^m$ into a subvariety $V$ of $\mathbb P^n(\mathbb C)$ with respect to an arbitrary family of slowly moving hypersurfaces $\mathcal…