Related papers: Geometric structures, the Gromov order, Kodaira di…

We present two geometric interpretations for complex multivectors and determinants: a little known one in terms of square roots of volumes, and a new one which uses fractions of volumes and allows graphical representations. The fraction…

We investigate the structure of smooth and horizonless microstate geometries in six dimensions, in the spirit of the five-dimensional analysis of Gibbons and Warner [arXiv:1305.0957]. In six dimensions, which is the natural setting for…

Generically an almost complex structure has no symmetries at all, but there exist symmetric structures. In this paper we describe how to guarantee that the pseudogroup of local symmetries is small (finite-dimensional). It will be indicated…

Following a method introduced by Thomas-Vasquez and developed by Grundman, we prove that many Hilbert modular threefolds of arithmetic genus $0$ and $1$ are of general type, and that some are of nonnegative Kodaira dimension. The new…

The simplicial volume is a homotopy invariant of oriented closed connected manifolds measuring the efficiency of representing the fundamental class by singular chains with real coefficients. Despite of its topological nature, the simplicial…

We construct a basis of the space ${\text S}_{14}({\text{Sp}}_{12}({\mathbb Z}))$ of Siegel cusp forms of degree $6$ and weight $14$ consisting of harmonic theta series. One of these functions has vanishing order $2$ at the boundary which…

We express the Kodaira-Iitaka dimension and the multiplicity of graded linear series in terms of the intersection theory of the plurisubharmonic envelope associated with the linear series, and obtain two refined versions of these formulas…

For $\Gamma_1$-structures on 3-manifolds, we give a very simple proof of Thurston's regularization theorem, first proved in \cite{thurston}, without using Mather's homology equivalence. Moreover, in the co-orientable case, the resulting…

We prove several results on the additivity of Kodaira dimension under smooth morphisms of smooth projective varieties.

In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…

We consider asymptotic dimension of coarse spaces. We analyse coarse structures induced by metrisable compactifications. We calculate asymptotic dimension of coarse cell complexes. We calculate the asymptotic dimension of certain negatively…

Based on the celebrated result on zeros of holomorphic 1-forms on complex varieties of general type by Popa and Schnell, we study holomorphic 1-forms on $n$-dimensional varieties of Kodaira dimension $n-1$. We show that a complex minimal…

In this note we discuss the effect of the symplectic sum along spheres in symplectic four-manifolds on the Kodaira dimension of the underlying symplectic manifold. We find that the Kodaira dimension is non-decreasing. Moreover, we are able…

This is the first of a series of papers, in which we study the plurigenera, the Kodaira dimension and more generally the Iitaka dimension on compact almost complex manifolds. Based on the Hodge theory on almost complex manifolds, we…

In this article, we present what we believe to be a simple way to motivate the use of Hilbert spaces in quantum mechanics. To achieve this, we study the way the notion of dimension can, at a very primitive level, be defined as the…

In this paper, we prove that the systolic volume of a closed aspherical 3-manifold is bounded below in terms of complexity. Systolic volume is defined as the optimal constant in a systolic inequality. Babenko showed that the systolic volume…

We study holomorphic 2-forms on projective (or compact Kaehler) threefolds not of general type and prove that in almost all cases the 2-form is created by some standard process. This means roughly that every 2-form is induced by a…

Inspired by group cohomology, we define several coarse topological invariants of metric spaces. We define the coarse cohomological dimension of a metric space, and demonstrate that if G is a countable group, then the coarse cohomological…

We give a spinorial construction of Sasakian and 3-Sasakian structures in arbitrary dimension, generalizing previously known results in dimensions 5 and 7. Furthermore, we obtain a complete description of the space of invariant spinors on a…

It is shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism. The geometric structure of the variety is described by methods of equivariant lifting and…