scholarly journals Hilbert series of tangent cones for Gorenstein monomial curves in A^{4}(K)

2021 ◽  
Keyword(s):  
Hilbert Series ◽  
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 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

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

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