scholarly journals On the Apéry sets of monomial curves

2012 ◽  
Vol 86 (2) ◽  
pp. 289-320 ◽  
Author(s):  
Teresa Cortadellas Benítez ◽  
Raheleh Jafari ◽  
Santiago Zarzuela Armengou
Keyword(s):  
Monomial Curves ◽  
Apéry Sets

On the equations defining projective monomial curves

1998 ◽  
Vol 26 (6) ◽  
pp. 1907-1912 ◽  
Author(s):  
Margherita Barlie ◽  
Marcel Morales
Keyword(s):  
Monomial Curves

Bases and Ideal Generators for Projective Monomial Curves

2012 ◽  
Vol 40 (1) ◽  
pp. 173-191 ◽  
Author(s):  
Ping Li ◽  
D. P. Patil ◽  
Leslie G. Roberts
Keyword(s):  
Monomial Curves

Non-Cohen–Macaulay Projective Monomial Curves with Positive h-Vector

2005 ◽  
Vol 48 (2) ◽  
pp. 203-210 ◽  
Author(s):  
Victoria E. de Quehen ◽  
Leslie G. Roberts
Keyword(s):  
Infinite Family ◽  
Monomial Curves

AbstractWe find an infinite family of projective monomial curves all of which have h-vector with no negative values and are not Cohen–Macaulay.

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).

On the equations defining monomial curves

1994 ◽  
Vol 22 (7) ◽  
pp. 2639-2649 ◽  
Author(s):  
Apostolos Thoma
Keyword(s):  
Monomial Curves

Singularity of Monomial Curves in A3 and Gorenstein Monomial Curves in A4

1985 ◽  
Vol 37 (5) ◽  
pp. 872-892 ◽  
Author(s):  
Jürgen Kraft
Keyword(s):  
Correction Term ◽  
Milnor Number ◽  
Monomial Curves ◽  
Space Curves ◽  
Image Position ◽  
Monomial Curve

Let 2 ≦ s ∊ N and {n1, …, ns) ⊆ N*. In 1884, J. Sylvester [13] published the following well-known result on the singularity degree S of the monomial curve whose corresponding semigroup is S: = 〈n1, …, ns): If s = 2, thenLet K: = –Z\S andfor all 1 ≦ i ≦ s. We introduce the invariantof S involving a correction term to the Milnor number 2δ [4] of S. As a modified version and extension of Sylvester's result to all monomial space curves, we prove the following theorem: If s = 3, thenWe prove similar formulas for s = 4 if S is symmetric.

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.

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