Related papers: Kodaira Dimension in Low Dimensional Topology

This paper provides a comprehensive overview of the current state of research on Douglas curvature in Finsler spaces. It explores the significance, properties, and applications of Douglas curvature, and its role in understanding Finsler…

This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.

This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.

This paper is a sequel of Imamura (2019) (arXiv:1711.01609) where we set up a framework of nonstandard large-scale topology. In the present paper, we apply our framework to various topics in large-scale topology: spaces having with both…

We give a bound on the H-constants of configurations of smooth curves having transversal intersection points only on an algebraic surface of non-negative Kodaira dimension. We also study in detail configurations of lines on smooth complete…

We obtain an ordering of closed aspherical 4-manifolds that carry a non-hyperbolic Thurston geometry. As application, we derive that the Kodaira dimension of geometric 4-manifolds is monotone with respect to the existence of maps of…

The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…

The constraints on the models for the structure formation arising from various cosmological observations at different length scales are reviewed. The status of different models for structure formation is examined critically in the light of…

We give examples of measures on certain k-surfaces in R^d. These measures satisfy convolution estimates which are nearly optimal.

The massive topologically and self dual theories en seven dimensions are considered. The local duality between these theories is established and the dimensional reduction lead to the different dualities for massive antisymmetric fields in…

These notes contain a brief introduction to the construction of toric Calabi--Yau hypersurfaces and complete intersections with a focus on issues relevant for string duality calculations. The last two sections can be read independently and…

This is a quick survey of theoretical and experimental efforts to understand and identify the Odderon.

In this note, we introduce a new poset parameter called local $t$-dimension. We also discuss the fractional variants of this and other dimension-like parameters.

The properties of topological systems are inherently tied to their dimensionality. Higher-dimensional physical systems exhibit topological properties not shared by their lower dimensional counterparts and, in general, offer richer physics.…

This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.

This paper, written in relation to the Current Developments in Mathematics 2012 Conference, discusses the recent papers on perfectoid spaces. Apart from giving an introduction to their content, it includes some open questions, as well as…

In this thesis we discuss some aspects concerning the construction of a 4D effective theory derived from higher dimensional (in particular 6D) models. The first part is devoted to the study of how the heavy Kaluza-Klein modes contribute to…

We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.

We describe the induced geometry on several classes of Kodaira moduli spaces of rational curves in twistor spaces. By constructing connections and frames on the moduli spaces we build and review twistor theories pertaining to relativistic…

This review aims to provide a very short and pedestrian introduction to some of the basics of extra-dimensional physics. The hope is to facilitate access and to be, in some respects, complementary to the many already existing reviews on…