scholarly journals Tangent cones at curve and surface singularities

1994 ◽  
Vol 95 (2) ◽  
pp. 189-201 ◽  
Author(s):  
Akira Ooishi
Keyword(s):  
Tangent Cones ◽  
Surface Singularities

scholarly journals On Tangency in Equisingular Families of Curves and Surfaces

2020 ◽  
Vol 71 (2) ◽  
pp. 485-505
Author(s):  
Arturo Giles Flores ◽  
O N Silva ◽  
J Snoussi
Keyword(s):  
Parameter Space ◽  
Tangent Cones ◽  
Curves And Surfaces ◽  
Families Of Curves ◽  
The Family ◽  
Surface Singularities ◽  
Whitney Equisingularity

Abstract We study the behavior of limits of tangents in topologically equivalent spaces. In the context of families of generically reduced curves, we introduce the $s$-invariant of a curve and we show that in a Whitney equisingular family with the property that the $s$-invariant is constant along the parameter space, the number of tangents of each curve of the family is constant. In the context of families of isolated surface singularities, we show through examples that Whitney equisingularity is not sufficient to ensure that the tangent cones of the family are homeomorphic. We explain how the existence of exceptional tangents is preserved by Whitney equisingularity but their number can change.

scholarly journals Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

2017 ◽  
Vol 4 (1) ◽  
pp. 43-72 ◽  
Author(s):  
Martin de Borbon
Keyword(s):  
Vector Field ◽  
Einstein Metrics ◽  
Projective Line ◽  
Tangent Cones ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Complex Curves ◽  
Complex Dimensions ◽  
Irregular Case ◽  
Kähler Einstein Metrics

Abstract The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.

scholarly journals Topological Atomic Chains on 2D Hybrid Structure

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3289
Author(s):  
Tomasz Kwapiński ◽  
Marcin Kurzyna
Keyword(s):  
Tight Binding ◽  
Wide Band ◽  
Hybrid Structure ◽  
Spectral Density Function ◽  
Hybrid Structures ◽  
Function Technique ◽  
Edge States ◽  
Surface Singularities ◽  
Atomic Chains ◽  
Topological States

Mid-gap 1D topological states and their electronic properties on different 2D hybrid structures are investigated using the tight binding Hamiltonian and the Green’s function technique. There are considered straight armchair-edge and zig-zag Su–Schrieffer–Heeger (SSH) chains coupled with real 2D electrodes which density of states (DOS) are characterized by the van Hove singularities. In this work, it is shown that such 2D substrates substantially influence topological states end evoke strong asymmetry in their on-site energetic structures, as well as essential modifications of the spectral density function (local DOS) along the chain. In the presence of the surface singularities the SSH topological state is split, or it is strongly localized and becomes dispersionless (tends to the atomic limit). Additionally, in the vicinity of the surface DOS edges this state is asymmetrical and consists of a wide bulk part together with a sharp localized peak in its local DOS structure. Different zig-zag and armachair-edge configurations of the chain show the spatial asymmetry in the chain local DOS; thus, topological edge states at both chain ends can appear for different energies. These new effects cannot be observed for ideal wide band limit electrodes but they concern 1D topological states coupled with real 2D hybrid structures.

Reduced Tangent Cones and Conductor at Multiplanar Isolated Singularities

2008 ◽  
Vol 36 (8) ◽  
pp. 2969-2978 ◽  
Author(s):  
Alessandro De Paris ◽  
Ferruccio Orecchia
Keyword(s):  
Tangent Cones ◽  
Isolated Singularities

scholarly journals ON -K2 FOR NORMAL SURFACE SINGULARITIES

1998 ◽  
Vol 09 (06) ◽  
pp. 653-668 ◽  
Author(s):  
HAO CHEN ◽  
SHIHOKO ISHII
Keyword(s):  
Lower Bound ◽  
Positive Integer ◽  
Rational Number ◽  
Accumulation Point ◽  
Normal Surface ◽  
Accumulation Points ◽  
Surface Singularities

In this paper we show the lower bound of the set of non-zero -K2 for normal surface singularities establishing that this set has no accumulation points from above. We also prove that every accumulation point from below is a rational number and every positive integer is an accumulation point. Every rational number can be an accumulation point modulo ℤ. We determine all accumulation points in [0, 1]. If we fix the value -K2, then the values of pg, pa, mult, embdim and the numerical indices are bounded, while the numbers of the exceptional curves are not bounded.

scholarly journals Infinitesimal deformations of quotient surface singularities

1988 ◽  
Vol 20 (1) ◽  
pp. 31-66 ◽  
Author(s):  
Kurt Behnke ◽  
Constantin Kahn ◽  
Oswald Riemenschneider
Keyword(s):  
Quotient Surface ◽  
Surface Singularities ◽  
Infinitesimal Deformations
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