Related papers: Bijectiveness of the Nash Map for Quasi-Ordinary H…
Given a quasi-compact, quasi-separated scheme X, a bijection between the tensor localizing subcategories of finite type in Qcoh(X) and the set of all subsets $Y\subseteq X$ of the form $Y=\bigcup_{i\in\Omega}Y_i$, with $X\setminus Y_i$…
The author has been interested in regions surrounded by cylinders of real algebraic hypersurfaces and their shapes and polynomials associated to them. Here, we formulate and investigate natural decompositions into such cylinders of real…
We employ the formalism of vanishing cycles and perverse sheaves to introduce and study the vanishing cohomology of complex projective hypersurfaces. As a consequence, we give upper bounds for the Betti numbers of projective hypersurfaces,…
For some class of mappings, which are generalization of space quasiisometries, an upper estimate for a measure of image of a ball is obtained. As consequence, it is obtained one analog of Schwartz lemma for mappings mentioned above. Results…
Let d be a positive integer. We show a finiteness theorem for semialgebraic RL triviality of a Nash family of Nash functions defined on a Nash manifold, generalising Benedetti-Shiota's finiteness theorem for semialgebraic RL equivalence…
In this survey paper we give a proof of hyperbolicity of the complex of curves for a non-exceptional surface S of finite type combining ideas of Masur/Minsky and Bowditch. We also shortly discuss the relation between the geometry of the…
Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give…
The goal of this work is to prove the regularity of certain quasi-plurisubharmonic upper envelopes. Such envelopes appear in a natural way in the construction of hermitian metrics with minimal singularities on a big line bundle over a…
In this paper we present a rigidity theorem for locally isometric hypersurfaces with a curvature restriction in de Sitter space. This is an analogue to the case for Riemannian space forms given by Guan and Shen in [5].
We provide normal forms for singularities of analytic hypersurfaces in $({\mathbb C}^n,0)$, using holomorphic vector fields.
We study in this paper quasiperiodic maximal surfaces in pseudo-hyperbolic spaces and show that they are characterised by a curvature condition, Gromov hyperbolicity or conformal hyperbolicity. We show that the limit curves of these…
We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.
We consider closed biharmonic hypersurfaces in the Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula involving the position vector for biharmonic…
Given an irreducible hypersurface singularity of dimension $d$ (defined by a polynomial $f\in K[[ {\bf x} ]][z]$) and the projection to the affine space defined by $K[[ {\bf x} ]]$, we construct an invariant which detects whether the…
We introduce a dual logarithmic residue map for hypersurface singularities and use it to answer a question of Kyoji Saito. Our result extends a theorem of L\^e and Saito by an algebraic characterization of hypersurfaces that are normal…
The purpose of this article is to study Lipschitz CR mappings from an $h$-extendible (or semi-regular) hypersurface in $\mbb C^n$. Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A…
The fundamental aim of this paper is to introduce and investigate a new property of quasi 2-normed space based on a question given by C. Park (2006) [2] for the completion quasi 2-normed space. Finally, we also find an answer for a question…
After quick survey of some key results and open questions about the structure of singularities of minimal surfaces, we discuss recent work~\cite{Sim23} on singularities of stable minimal hypersurfaces, including some simplifications of the…
It is shown that every C-semianalytic arc-symmetric set can be realized as the zero locus of an arc-analytic function. As a consequence, a Nash globally subanalytic arc-symmetric set is the zero locus of a continuous globally-subanalytic…
In this semi-expository paper we review the notion of a spherical space. In particular we present some recent results of Wedhorn on the classification of spherical spaces over arbitrary fields. As an application, we introduce and classify…