We present a classification of 2-dimensional, taut, Stein manifolds with a proper $R$-action. For such manifolds the globalization with respect to the induced local $C$-action turns out to be Stein. As an application we determine all 2-dimensional taut, non-complete, Hartogs domains over a Riemann surface.
In this paper we investigate a topological characterization of the Runge theorem in the Clifford algebra $ mathbb{R}_3$ via the description of the homology groups of axially symmetric open subsets of the quadratic cone in $mathbb{R}_3$.
We will show that any open Riemann surface $M$ of finite genus is biholomorphic to an open set of a compact Riemann surface. Moreover, we will introduce a quotient space of forms in $M$ that determines if $M$ has finite genus and also the minimal genus where $M$ can be holomorphically embedded.
In this paper we construct open Stein neighbourhoods of compact sets of the form $Acup K$ in a complex space, where $K$ is a compact holomorphically convex set, $A$ is a compact complex curve with boundary $bA$ of class $mathscr C^2$ which may intersect $K$, and $Acap K$ is $mathscr O(A)$-convex.
In this paper we prove that if two normal affine surfaces $S$ and $S$ have isomorphic automophism groups, then every connected algebraic group acting regularly and faithfully on $S$ acts also regularly and faithfully on $S$. Moreover, if $S$ is non-toric, we show that the dynamical type of a 1-torus action is preserved in presence of an additive group action. We also show that complex affine toric surfaces are determined by the abstract group structure of their regular automorphism groups in the category of complex normal affine surfaces using properties of the Cremona group. As a generalization to arbitrary dimensions, we show that complex affine toric varieties, with the exception of the algebraic torus, are uniquely determined in the category of complex affine normal varieties by their automorphism groups seen as ind-groups.