scholarly journals Note on the monodromy conjecture for a space monomial curve with a plane semigroup

2020 ◽  
Vol 358 (2) ◽  
pp. 177-187
Author(s):  
Jorge Martín-Morales ◽  
Hussein Mourtada ◽  
Willem Veys ◽  
Lena Vos
Keyword(s):  
Monodromy Conjecture ◽  
Monomial Curve

scholarly journals The monodromy conjecture for a space monomial curve with a plane semigroup

2021 ◽  
Vol 65 ◽  
pp. 529-597
Author(s):  
Jorge Martín-Morales ◽  
Willem Veys ◽  
Lena Vos
Keyword(s):  
Monodromy Conjecture ◽  
Monomial Curve

scholarly journals An algorithm for checking whether the toric ideal of an affine monomial curve is a complete intersection

2007 ◽  
Vol 42 (10) ◽  
pp. 971-991 ◽  
Author(s):  
Isabel Bermejo ◽  
Ignacio García-Marco ◽  
Juan José Salazar-González
Keyword(s):  
Complete Intersection ◽  
Toric Ideal ◽  
Monomial Curve

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).

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.

scholarly journals An affine monomial curve with irrational Poincaré–Betti series

2000 ◽  
Vol 152 (1-3) ◽  
pp. 89-92 ◽  
Author(s):  
Ralf Fröberg ◽  
Jan-Erik Roos
Keyword(s):  
Monomial Curve

scholarly journals The $\mathcal{A}$ -hypergeometric system associated with a monomial curve

1999 ◽  
Vol 99 (2) ◽  
pp. 179-207 ◽  
Author(s):  
Eduardo Cattani ◽  
Carlos D?Andrea ◽  
Alicia Dickenstein
Keyword(s):  
Monomial Curve
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