Related papers: Sufficiency of non-isolated singularities

The goal of this paper is to establish a new characterization of quasi-homogeneous isolated singularities of free curves and nearly free curves $C$ in $\mathbb{P}_\mathbb{C}^2$. The criterion will be in terms of a first syzygy matrix…

Consider a compact Lie group $G$ and a closed subgroup $H<G$. Suppose $\mathcal M$ is the set of $G$-invariant Riemannian metrics on the homogeneous space $M=G/H$. We obtain a sufficient condition for the existence of $g\in\mathcal M$ and…

We show that for certain integers $n$, the problem of whether or not a Cayley digraph $\Gamma$ of $\mathbb Z_n$ is also isomorphic to a Cayley digraph of some other abelian group $G$ of order $n$ reduces to the question of whether or not a…

we obtain a necessary condition for the character degree graph with all of its vertices are odd degree of a finite solvable group G.

We study the massless scalar field on asymptotically flat spacetimes with closed timelike curves (CTC's), in which all future-directed CTC's traverse one end of a handle (wormhole) and emerge from the other end at an earlier time. For a…

Given a locally compact Polish space X, a necessary and sufficient condition for a group G of homeomorphisms of X to be the full isometry group of (X,d) for some proper metric d on X is given. It is shown that every locally compact Polish…

Two graphs having the same spectrum are said to be cospectral. Two graphs such that the absolute values of their nonzero eigenvalues coincide are singularly cospectral graphs. Cospectrality implies singular cospectrality, but the converse…

Let $X, Y$ be complete, simply connected Riemannian surfaces with pinched negative curvature $-b^2 \leq K \leq -1$. We show that if $f : \partial X \to \partial Y$ is a Moebius homeomorphism between the boundaries at infinity of $X, Y$,…

For a (molecular) graph $G$ and any real number $\alpha\ne 0$ , the zero-order general Randi\'c index , denote by $^0R_\alpha$, is defined by the following equation: \begin{align*} {^0R_\alpha} (G) =\sum_{v\in G}d_G (v) ^{\alpha} (\alpha…

In this paper, two sufficient and necessary conditions are given. The first one characterizes when the boundary path groupoid of a topological graph without singular vertices has closed interior of its isotropy group bundle, and the second…

According to [8] if the stationary Schroedinger equation on n-dim. Riemann space admits R-separation of variables (i.e. separation of variables with a factor R), then the underlying metric is necessarily isothermic. An important sub-class…

We prove that for a normal projective variety $X$ in characteristic 0, and a base-point free ample line bundle $L$ on it, the restriction map of divisor class groups $\Cl(X)\to \Cl(Y)$ is an isomorphism for a general member $Y\in |L|$…

We consider germs of holomorphic vector fields at a fixed point having a nilpotent linear part at that point, in dimension $n \geq 3$. Based on Belitskii's work, we know that such a vector field is formally conjugate to a (formal) normal…

At a finite-time singularity of harmonic map flow in the critical dimension, we show that a Lojasiewicz inequality between the quantities appearing in Struwe's monotonicity formula implies continuity of the body map and the no-neck property…

Sufficient conditions for a simple graph to be characterized up to isomorphism given its spectrum and the spectrum of its complement graph are known due to Wang and Xu. This note establishes a related sufficient condition in the presence of…

Let $(\bf {V,0})\subset (\mathbb{C}^n,0)$ be a germ of a complex hypersurface and let $f: (\mathbb{C}^n,0)\to(\mathbb{C}^n,0)$ be a germ of a finite holomorphic mapping. If germs $(\bf {V,0})$ and ${\bf W}:=(F^{-1}(\bf{ V})),0)$ are…

Let $R$ be a semilocal geometrically factorial Noetherian domain of characteristic zero. We show that a reductive $R$-group scheme is isotropic if it is generically isotropic. We derive various consequences, in particular for the…

We present necessary and sufficient conditions for an n\times n complex matrix B to be unitarily similar to a fixed unicellular (i.e., indecomposable by similarity) n\times n complex matrix A

We introduce the class of $n$-extremal holomorphic maps, a class that generalises both finite Blaschke products and complex geodesics, and apply the notion to the finite interpolation problem for analytic functions from the open unit disc…

We show that for any $N>0$ there exists a natural even $n>N$ such that the discriminant of moduli of K3 surfaces of the degree $n$ is not equal to the set of zeros of any automorphic form on the corresponding IV type domain. We give the…