Lack of convexity for tangent cones of needle variations

2003 ◽  
Author(s):  
R.-M. Bianchini ◽  
M. Kawski
Keyword(s):  
Tangent Cones ◽  
Needle Variations

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.

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 Complete Intersection Monomial Curves and the Cohen—Macaulayness of Their Tangent Cones

2019 ◽  
Vol 26 (04) ◽  
pp. 629-642
Author(s):  
Anargyros Katsabekis
Keyword(s):  
Complete Intersection ◽  
Tangent Cone ◽  
Affine Space ◽  
Intersection Property ◽  
Tangent Cones ◽  
Monomial Curves ◽  
Monomial Curve

Let C(n) be a complete intersection monomial curve in the 4-dimensional affine space. In this paper we study the complete intersection property of the monomial curve C(n + wv), where w > 0 is an integer and v ∈ ℕ4. In addition, we investigate the Cohen–Macaulayness of the tangent cone of C(n + wv).

scholarly journals On the Cohen-Macaulay Property for Quadratic Tangent Cones

10.37236/5793 ◽  
2016 ◽  
Vol 23 (3) ◽  
Author(s):  
Dumitru I. Stamate
Keyword(s):  
Tangent Cone ◽  
Gröbner Basis ◽  
Numerical Semigroup ◽  
Tangent Cones ◽  
Grobner Basis

Let $H$ be an $n$-generated numerical semigroup such that its tangent cone $\operatorname{gr}_\mathfrak{m} K[H]$ is defined by quadratic relations. We show that if $n<5$ then $\operatorname{gr}_\mathfrak{m} K[H]$ is Cohen-Macaulay, and for $n=5$ we explicitly describe the semigroups $H$ such that $\operatorname{gr}_\mathfrak{m} K[H]$ is not Cohen-Macaulay. As an application we show that if the field $K$ is algebraically closed and of characteristic different from two, and $n\leq 5$ then $\operatorname{gr}_\mathfrak{m} K[H]$ is Koszul if and only if (possibly after a change of coordinates) its defining ideal has a quadratic Gröbner basis.

Tangent Cones and Tangent Sets

2014 ◽  
pp. 109-211
Author(s):  
Akhtar A. Khan ◽  
Christiane Tammer ◽  
Constantin Zălinescu
Keyword(s):  
Tangent Cones ◽  
Tangent Sets
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