Related papers: Weakly complete complex surfaces

We construct topological invariants, called abstract weak orbit spaces, of flows and homeomorphisms on topological spaces, to describe both gradient dynamics and recurrent dynamics. In particular, the abstract weak orbit spaces of flows on…

We prove that square integrable holomorphic functions (with respect to a plurisubharmonic weight) can be extended in a square integrable manner from certain singular hypersurfaces (which include uniformly flat, normal crossing divisors) to…

We show that every strictly pseudoconvex domain $\Omega$ with smooth boundary in a complex manifold $\mathcal{M}$ admits a global defining function, i.e., a smooth plurisubharmonic function $\varphi \colon U \to \mathbb R$ defined on an…

We prove for a morphism $f \colon X \rightarrow S$ locally of $^+$weakly finite type, separated and taut, where $X$ is a weakly square complete adic space and $S$ a square complete and stable adic space, there exists a universal vertical…

We introduce the complete lifts of maps between (real and complex) Euclidean spaces and study their properties concerning holomorphicity, harmonicity and horizontal weakly conformality. As applications, we are able to use this concept to…

The purpose of this paper is to generalize in a geometric setting theorems of Severi, Brown and Bochner about analytic continuation of real analytic functions which are holomorphic or harmonic with respect to one of its variables. We prove…

We propose the study of a conformally invariant functional for surfaces of complex projective plane which is closely related to the classical Willmore functional. We show that minimal surfaces of complex projective plane are critical for…

This article generalizes the result of Katzarkov and Ramachandran from algebraic surfaces to K\"ahler surfaces. We follow their argument to prove the holomorphic convexity of a reductive Galois covering over a compact K\"ahler surface which…

We address the problem of weak approximation for general cubic hypersurfaces defined over number fields, with arbitrary singular locus. In particular, weak approximation is established for the smooth locus of projective, geometrically…

We address weak approximation for certain del Pezzo surfaces defined over the function field of a curve. We study the rational connectivity of the smooth locus of degree two del Pezzo surfaces with two A1 singularities in order to prove…

We classify singular holomorphic vector fields in two-dimensional complex space admitting a (Levi-nonflat) real-analytic invariant 3-fold through the singularity. In this way, we complete the classification of infinitesimal symmetries of…

A semiholomorphic foliations of type (n, d) is a differentiable real manifold X of dimension 2n + d, foliated by complex leaves of complex dimension n. In the present work, we introduce an appropriate notion of pseudoconvexity (and…

The main message of the paper is that for Gorenstein singularities, whose (real) link is rational homology sphere, the Artin--Laufer program can be continued. Here we give the complete answer in the case of elliptic singularities. The main…

We define a complex connection on a real hypersurface of $\C^{n+1}$ which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify connected real hypersurfaces in $\C^{n+1}$, $n\ge 2$, which are…

Let $V$ be a complete discrete valuation ring with residue field $k$ of positive characteristic and with fraction field $K$ of characteristic 0. We clarify the analysis behind the Monsky--Washnitzer completion of a commutative $V$-algebra…

Given a continuous, radial, rapidly decreasing weight $v$ on the complex plane $\mathbf{C}$, we study the solid hull of its associated weighted space $H_v^\infty(\mathbf{C})$ of all the entire functions $f$ such that $v|f|$ is bounded. The…

Let $(\phi_t)$ be an area-preserving smooth flow on a compact, connected, orientable surface $\mathcal M$ with at least one but finitely many fixed points. Assume that $(\phi_t)$ is analytic (up to a canonical change of coordinates) in the…

Let $X$ be a compact K\"ahler manifold and $\theta$ a smooth closed $(1,1)$-real form representing a big cohomology class $\alpha \in H^{1,1}(X,\R)$. The purpose of this note is to show, using pluripotential and viscosity techniques, that…

We study the cohomology of a general stable sheaf on an abelian surface. We say that a moduli space satisfies weak Brill-Noether if the general sheaf has at most one non-zero cohomology group. Let $(X,H)$ be a polarized abelian surface and…

It is shown that a superconformal surface with arbitrary codimension in flat Euclidean space has a (necessarily unique) dual superconformal surface if and only if the surface is S-Willmore, the latter a well-known necessary condition to…