scholarly journals On the Cohen–Macaulayness of tangent cones of monomial curves inA4(K)

2019 ◽  
Vol 43 (3) ◽  
pp. 1425-1446
Author(s):  
Feza ARSLAN ◽  
Anargyros KATSABEKIS ◽  
Melissa NALBANDIYAN
Keyword(s):  
Tangent Cones ◽  
Monomial Curves

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 LIFTINGS OF A MONOMIAL CURVE

2018 ◽  
Vol 98 (2) ◽  
pp. 230-238
Author(s):  
MESUT ŞAHİN
Keyword(s):  
Tangent Cone ◽  
Tangent Cones ◽  
Monomial Curves ◽  
Original Curve ◽  
Monomial Curve

We study an operation, that we call lifting, creating nonisomorphic monomial curves from a single monomial curve. Our main result says that all but finitely many liftings of a monomial curve have Cohen–Macaulay tangent cones even if the tangent cone of the original curve is not Cohen–Macaulay. This implies that the Betti sequence of the tangent cone is eventually constant under this operation. Moreover, all liftings have Cohen–Macaulay tangent cones when the original monomial curve has a Cohen–Macaulay tangent cone. In this case, all the Betti sequences are just the Betti sequence of the original curve.

scholarly journals Tangent cones of monomial curves obtained by numerical duplication

2019 ◽  
Vol 70 (3) ◽  
pp. 461-477
Author(s):  
Marco D’Anna ◽  
Raheleh Jafari ◽  
Francesco Strazzanti
Keyword(s):  
Tangent Cones ◽  
Monomial Curves ◽  
Numerical Duplication

scholarly journals On the multiplicity of tangent cones of monomial curves

2019 ◽  
Vol 57 (1) ◽  
pp. 215-225
Author(s):  
Alessio Sammartano
Keyword(s):  
Tangent Cones ◽  
Monomial Curves

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.

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