Related papers: Beyond Mumford's theorem on normal surfaces

The weight two ordinary deformations are unobstructed in the cyclotomic limit under certain assumptions. We show that such an ordinary deformation ring over the cyclotomic tower can have arbitrarily large dimension.

We establish a lower bound for the surface area of a closed, convex hypersurface in Euclidean space in terms of its displacement under continuous maps. As a result, a hypothesized lower bound for the volume of a Riemannian $n$-sphere,…

The purpose of this paper is twofold. First, we survey known results about theta dualities on moduli spaces of sheaves on curves and surfaces. Secondly, we establish new such dualities in the surface case. Among others, the case of elliptic…

This informal note collects key results and open problems on the (co)homology of the Deligne-Mumford moduli spaces of real marked rational curves. The open problems are both of topological nature, aiming to investigate the (co)homology of…

Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.

We study relations of some classes of $k$-convex, $k$-visible bodies in Euclidean spaces. We introduce and study \textrm{circular projections} in normed linear spaces and classes of bodies related with families of such maps, in particular,…

This contribution presents the cosmological models with extra dimensions that have been recently elaborated, which assume that ordinary matter is confined on a surface, called brane, embedded in a higher dimensional spacetime.

We discuss the status of the SM - The principles - The Lagrangian - The problems - Open questions - The ways beyond. Then we consider possible physics beyond the SM - New symmetries (Gauge, SUSY, etc) - New particles (gauge, axion,…

The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.

We remark some basic facts on homological aspects of involutive Lie bialgebras and their involutive bimodules, and present some problems on surface topology related to these facts.

Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with…

We construct a smooth complex projective rational surface with infinitely many mutually non-isomorphic real forms. This gives the first definite answer to a long standing open question if a smooth complex projective rational surface has…

Despite its continued observational successes, there is a persistent (and growing) interest in extending cosmology beyond the standard model, $\Lambda$CDM. This is motivated by a range of apparently serious theoretical issues, involving…

2-stratifolds are a generalization of 2-manifolds in that there are disjoint simple closed curves where several sheets meet. They arise in the study of categorical invariants of 3-manifolds and may have applications to topological data…

The explicit coordinate transformations which show the equivalence between a four-dimensional spatially flat cosmology and an appropriate submanifold in the flat five-dimensional Minkowski space-time are presented. Analogous procedure is…

The set of matrix tuples with invariant subspaces whose dimensions sum up to the dimension of the space, but which do not span the whole space form an algebraic hypersurface. We found the equation of this hypersurface. This generalizes…

We investigated singular points of translation surfaces under the linearly independent condition. In this paper, as completion, we investigate singular points of translation surfaces under the linearly dependent condition, using the…

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 present several results of embedding type for parabolic Morrey spaces with or without mixed norms. Some other interpolation results for parabolic Morrey spaces are also given.

I briefly summarize the prospects for extending our understanding of physics beyond the standard model within the next five years.