Related papers: Twistor structures, tt*-geometry and singularity t…

Geometrical structures intrinsic to non-expanding, weakly isolated and isolated horizons are analyzed and compared with structures which arise in other contexts within general relativity, e.g., at null infinity. In particular, we address in…

We characterize HKT structure in terms of nondegenrate complex Poisson bivector on hypercomplex manifold. We extend the characterization to the twistor space. After considering the flat case in detail, we show that the twistor space of…

We give a survey on some aspects of the topological investigation of isolated singularities of complex hypersurfaces by means of Picard-Lefschetz theory. We focus on the concept of distinguished bases of vanishing cycles and the concept of…

This note emphasizes the role of multi-scale wave structures and junction conditions in many fields of physics, from the dynamics of fluids with non-convex equations of state to the study of gravitational singularities and bouncing…

According to a well-known theorem of Brieskorn and Slodowy, the intersection of the nilpotent cone of a simple Lie algebra with a transverse slice to the subregular nilpotent orbit is a simple surface singularity. At the opposite extremity…

In this paper, we construct tools from the holomorphic twistor spaces that we introduced in \cite{Gindi1} to derive results about the complex geometries of their base manifolds. In particular, we develop a new approach to studying…

The topological structure of the lines of principal curvature, the umbilic and partially umbilic singularities of all tridimensional ellipsoids of ${\mathbb R}^4$ is described.

This article shows how box dimension of the unit-time map can be used in studying the multiplicity of nilpotent singularities of planar vector fields. Using unit-time map on the characteristic curve of nilpotent singularity we define…

The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry \`a la Hitchin). The generalized twistor space associated to such a manifold is…

In this paper, we construct recollements and ladders for Brieskorn-Pham singularities via reduction/insertion functors, and study the singularity categories of the Brieskorn-Pham singularities using these ladders. In particular, we…

In this work a proposal for definition of twistors on generic curved spaces is exposed and investigated. We consider superpositions of nearly autoparallel and nearly geodesic maps (nearly conformal maps, nc-maps) of (pseudo-)Riemannian…

We are concerned with rigid analytic geometry in the general setting of Henselian fields $K$ with separated analytic structure, whose theory was developed by Cluckers--Lipshitz--Robinson. It unifies earlier work and approaches of numerous…

Transport twistor spaces are degenerate complex $2$-dimensional manifolds $Z$ that complexify transport problems on Riemannian surfaces, appearing, e.g., in geometric inverse problems. This article considers maps $\beta\colon Z\to…

We consider the topology for a class of hypersurfaces with highly nonisolated singularites which arise as exceptional orbit varieties of a special class of prehomogeneous vector spaces, which are representations of linear algebraic groups…

This is a survey article prepared for the submission to "Handbook of moduli". The following topics are discussed: (i) Basic facts and examples of resolutions for nilpotent orbit (ii) Q-factorial terminalizations of nilpotent orbit closures…

The paper collects different approaches and viewpoints on bilinear forms and hermitian forms around isolated hypersurface singularities. It gives the relations between them in precise formulas. It does not contain new results.

Using minimalist assumptions we develop a natural functional decomposition for the spacetime metric, and explicit tractable formulae for the surface gravities, in arbitrary stationary circular (PT symmetric) axisymmetric spacetimes. We…

Let $X=\overline{X}-D$ be a smooth quasi-projective curve. In arXiv:2110.12300 we constructed a Deligne-Hitchin modui space with Hecke gauge groupoid for connections of rank $2$. We extend this construction to the case of any rank $r$,…

Isolated hypersurface singularities come equipped with a Milnor lattice, a ${\mathbb Z}$-lattice of finite rank, and a set of $distinguished$ ${\mathbb Z}$-bases of this lattice. Usually these bases are constructed from $one$ morsification…

In this note we study numerically the combinatorics of curves and geodesics on the torus with one boundary component. A potential computational difficulty is avoided by counting inside specific orbits of the mapping class group up to a…