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

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

Comptes Rendus. Mathématique ◽

10.5802/crmath.30 ◽

2020 ◽

Vol 358 (2) ◽

pp. 177-187

Author(s):

Jorge Martín-Morales ◽

Hussein Mourtada ◽

Willem Veys ◽

Lena Vos

Keyword(s):

Monodromy Conjecture ◽

Monomial Curve

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On the derivations of the homogeneous coordinate ring of a monomial curve in Pdk

Communications in Algebra ◽

10.1080/00927879208824515 ◽

1992 ◽

Vol 20 (11) ◽

pp. 3279-3300 ◽

Cited By ~ 1

Author(s):

S. Molinelli ◽

G. Tamone

Keyword(s):

Coordinate Ring ◽

Monomial Curve

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

Journal of Symbolic Computation ◽

10.1016/j.jsc.2007.08.005 ◽

2007 ◽

Vol 42 (10) ◽

pp. 971-991 ◽

Cited By ~ 12

Author(s):

Isabel Bermejo ◽

Ignacio García-Marco ◽

Juan José Salazar-González

Keyword(s):

Complete Intersection ◽

Toric Ideal ◽

Monomial Curve

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

Algebra Colloquium ◽

10.1142/s1005386719000464 ◽

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).

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

Canadian Journal of Mathematics ◽

10.4153/cjm-1985-047-8 ◽

1985 ◽

Vol 37 (5) ◽

pp. 872-892 ◽

Cited By ~ 7

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.

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LIFTINGS OF A MONOMIAL CURVE

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972718000400 ◽

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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