2019
DOI: 10.3906/mat-1903-15
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Minimal free resolutions of the tangent cones for Gorenstein monomial curves

Abstract: We study the minimal free resolution of the tangent cone of Gorenstein monomial curves in affine 4-space. We give the explicit minimal free resolution of the tangent cone of noncomplete intersection Gorenstein monomial curve whose tangent cone has five minimal generators and show that the possible Betti sequences are (1, 5, 6, 2) and (1, 5, 5, 1). Moreover, we compute the Hilbert function of the tangent cone of these families as a result.

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Cited by 5 publications
(7 citation statements)
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“…Case 1(b) : Suppose that I S is minimally generated by the polynomials (1, 5, 5, 1) and (1, 5, 6, 2) , as given in [11]. Here, the other possible condition α 3 > α 32 + α 34 will be considered.…”
Section: Betti Sequences Of Cohen-macaulay Tangent Conesmentioning
confidence: 99%
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“…Case 1(b) : Suppose that I S is minimally generated by the polynomials (1, 5, 5, 1) and (1, 5, 6, 2) , as given in [11]. Here, the other possible condition α 3 > α 32 + α 34 will be considered.…”
Section: Betti Sequences Of Cohen-macaulay Tangent Conesmentioning
confidence: 99%
“…Under the restriction α 2 ≤ α 21 + α 24 by Theorem 2.2 and one possible condition α 3 ≤ α 32 + α 34 , the Betti sequences for the Cohen-Macaulay tangent cone of C S are (1, 5, 5, 1) and (1, 5, 6, 2) , as given in [11].…”
Section: Betti Sequences Of Cohen-macaulay Tangent Conesmentioning
confidence: 99%
See 1 more Smart Citation
“…The conjecture is open for local rings corresponding to 4-generated symmetric semigroups with α 2 > α 21 + α 24 . For some recent work on the monotonicity of the Hilbert function, see [1][2][3][11][12][13].…”
Section: Introductionmentioning
confidence: 99%
“…Since homogeneous-type semigroups have Cohen-Macaulay tangent cones, we restrict our attention to monomial curves having Cohen-Macaulay tangent cones in this article. The problem of determining the Betti sequence for the tangent cone (see [12, Problem 9.9]) was studied for 4-generated symmetric monomial curves by Mete and Zengin [10]. In this paper, we focus on the next interesting case of 4-generated pseudo-symmetric monomial curves.…”
Section: Introductionmentioning
confidence: 99%