Related papers: On normal embedding of complex algebraic surfaces

We study various classes of real hypersurfaces that are not embeddable into more special hypersurfaces in higher dimension, such as spheres, real algebraic compact strongly pseudoconvex hypersurfaces or compact pseudoconvex hypersurfaces of…

In this article, we address the classification of smooth projective algebraic surfaces over complex numbers admitting algebraic semigroup structures. We give a full description of those surfaces $S$, which has at least one non-trivial…

We find new examples of complex surfaces with countably many non-isomorphic algebraic structures. Here is one such example: take an elliptic curve $E$ in $\mathbb P^2$ and blow up nine general points on $E$. Then the complement $M$ of the…

We provide several families of compact complex curves embedded in smooth complex surfaces such that no neighborhood of the curve can be embedded in an algebraic surface. Different constructions are proposed, by patching neighborhoods of…

Rationally convex topological embeddings of compact surfaces (closed or with boundary) into $\mathbb{C}^2$ are constructed.

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…

We consider a subanalytic subset A of a complex analytic manifold M (when M is viewed as a real manifold) and formulate conditions under which A is a complex analytic subset of M.

We give tables of noncompact real forms of maximal reductive subalgebras of complex simple Lie algebras of rank up to 8. These were obtained by computational methods that we briefly describe. We also discuss applications in theoretical…

Given a set $S$ of $n$ points in $\mathbb{R}^d$, a $k$-set is a subset of $k$ points of $S$ that can be strictly separated by a hyperplane from the remaining $n-k$ points. Similarly, one may consider $k$-facets, which are hyperplanes that…

We show that there are strictly pseudoconvex, real algebraic hypersurfaces in $\bC^{n+1}$ that cannot be locally embedded into a sphere in $\bC^{N+1}$ for any $N$. In fact, we show that there are strictly pseudoconvex, real algebraic…

We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…

The article surveys published and not yet published results about moduli spaces of algebraic surfaces.

We consider the problem of constructing semisimple subalgebras of real (semi-) simple Lie algebras. We develop computational methods that help to deal with this problem. Our methods boil down to solving a set of polynomial equations. In…

We apply methods of nonstandard mathematics in order to regard analytic geometry in a very different way. For example, complex spaces are seen to be the "standard part" of certain algebraic nonstandard schemes. We construct a category of…

Algorithms for embedding certain types of nilpotent subalgebras in maximal subalgebras of the same type are developed, using methods of real algebraic groups. These algorithms are applied to determine non-conjugate subalgebras of the…

Let X be an affine real algebraic set . We investigate on the theory of algebraically constructible functions on X and the description of the semi-algebraic subsets of X when we replace the polynomial functions on X by some rational…

We characterize analytic curves that contain non-trivial self-affine sets. We also prove that compact algebraic surfaces cannot contain non-trivial self-affine sets.

We study the algebraic boundary of a convex semi-algebraic set via duality in convex and algebraic geometry. We generalize the correspondence of facets of a polytope to the vertices of the dual polytope to general semi-algebraic convex…

We give series of explicit examples of Levi-nondegenerate real-analytic hypersurfaces in complex spaces that are not transversally holomorphically embeddable into hyperquadrics of any dimension. For this, we construct invariants attached to…

We construct examples of algebraic surfaces with interesting fundamental groups.