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Free resolutions for the tangent cones of some homogeneous pseudo symmetric monomial curves

Yıl 2023, Cilt: 72 Sayı: 1, 129 - 136, 30.03.2023
https://doi.org/10.31801/cfsuasmas.1117855

Öz

In this article, we study minimal graded free resolutions of Cohen-Macaulay tangent cones of some monomial curves associated to 4-generated pseudo symmetric numerical semigroups. We explicitly give the matrices in these minimal free resolutions.

Kaynakça

  • Barucci, V., Fröberg, R. and Şahin, M., On free resolutions of some semigroup rings, J. Pure Appl. Algebra, 218(6) (2014),1107-1116. https://doi.org/10.1016/j.jpaa.2013.11.007
  • Buchsbaum, D., Eisenbud, D., What makes a complex exact?, J. Algebra, 25 (1973), 259-268.
  • Eto, K., Almost Gorenstein monomial curves in affine four space, Journal of Algebra, 488 (2017), 362-387. https://doi.org/10.1016/j.jalgebra.2017.05.044
  • Greuel, G.-M., Pfister, G., and Schönemann, H., Singular 2.0. A Computer Algebra System for Polynomial Computations. Centre for Computer Algebra, University of Kaiserslautern (2001). http://www.singular.uni-kl.de
  • Gimenez, P., Sengupta, I. and Srinivasan, H., Minimal free resolution for certain affine monomial curves, Commutative Algebra and its Connections to Geometry (PASI 2009), A. Corso and C. Polini Eds, Contemp. Math., 555 (Amer. Math. Soc., 2011) 87–95. https://doi.org/10.1081/AGB-120021893
  • Gimenez, P., Sengupta, I. and Srinivasan H., Minimal graded free resolution for monomial curves defined by arithmetic sequences, Journal of Algebra, 388 (2013) 294-310. https://doi.org/10.1016/j.jalgebra.2013.04.026
  • Greuel, G.-M., Pfister, G., A Singular Introduction to Commutative Algebra, Springer-Verlag, (2002).
  • Herzog, J., Rossi, M.E., Valla, G., On the depth of the symmetric algebra, Trans. Amer. Math. Soc., 296 (2) (1986), 577-606.
  • Jafari, R., Zarzuela Armengou, S., Homogeneous numerical semigroups, Semigroup Forum, 97 (2018), 278–306. https://doi.org/10.1007/s00233-018-9941-6
  • Komeda, J., On the existence of Weierstrass points with a certain semigroup, Tsukuba J. Math., 6(2) (1982), 237-270.
  • Mete, P., Zengin, E.E., Minimal free resolutions of the tangent cones of Gorenstein monomial curves, Turkish Journal of Mathematics, 43 (2019), 2782-2793. https://doi.org/ 10.3906/mat-1903-15
  • Mete, P., Zengin, E.E., On minimal free resolution of the associated graded rings of certain monomial curves: new proofs in A4., Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 68(1) (2019), 1019–1029. https://doi.org/10.31801/cfsuasmas.501449
  • Sengupta, I., A minimal free resolution for certain monomial curves in A4, Comm. Algebra, 31(6) (2003), 2791–2809. https://doi.org/10.1081/AGB-120021893
  • Şahin, M., Şahin, N., On pseudo symmetric monomial curves, Communications in Algebra, 46(6) (2018), 2561-2573. https://doi.org/10.1080/00927872.2017.1392532
  • Şahin, M., Şahin, N., Betti numbers for certain Cohen-Macaulay tangent cones, Bull. Aust. Math. Soc., 99(1) (2019), 68–77. doi:10.1017/S0004972718000898
  • Stamate, D., Betti numbers for numerical semigroup rings, Multigraded Algebra and Applications-NSA 24,2016, Springer Proceedings in Mathematics and Statistics, 238 (eds.V. Ene and E. Miller) (2018)
Yıl 2023, Cilt: 72 Sayı: 1, 129 - 136, 30.03.2023
https://doi.org/10.31801/cfsuasmas.1117855

Öz

Kaynakça

  • Barucci, V., Fröberg, R. and Şahin, M., On free resolutions of some semigroup rings, J. Pure Appl. Algebra, 218(6) (2014),1107-1116. https://doi.org/10.1016/j.jpaa.2013.11.007
  • Buchsbaum, D., Eisenbud, D., What makes a complex exact?, J. Algebra, 25 (1973), 259-268.
  • Eto, K., Almost Gorenstein monomial curves in affine four space, Journal of Algebra, 488 (2017), 362-387. https://doi.org/10.1016/j.jalgebra.2017.05.044
  • Greuel, G.-M., Pfister, G., and Schönemann, H., Singular 2.0. A Computer Algebra System for Polynomial Computations. Centre for Computer Algebra, University of Kaiserslautern (2001). http://www.singular.uni-kl.de
  • Gimenez, P., Sengupta, I. and Srinivasan, H., Minimal free resolution for certain affine monomial curves, Commutative Algebra and its Connections to Geometry (PASI 2009), A. Corso and C. Polini Eds, Contemp. Math., 555 (Amer. Math. Soc., 2011) 87–95. https://doi.org/10.1081/AGB-120021893
  • Gimenez, P., Sengupta, I. and Srinivasan H., Minimal graded free resolution for monomial curves defined by arithmetic sequences, Journal of Algebra, 388 (2013) 294-310. https://doi.org/10.1016/j.jalgebra.2013.04.026
  • Greuel, G.-M., Pfister, G., A Singular Introduction to Commutative Algebra, Springer-Verlag, (2002).
  • Herzog, J., Rossi, M.E., Valla, G., On the depth of the symmetric algebra, Trans. Amer. Math. Soc., 296 (2) (1986), 577-606.
  • Jafari, R., Zarzuela Armengou, S., Homogeneous numerical semigroups, Semigroup Forum, 97 (2018), 278–306. https://doi.org/10.1007/s00233-018-9941-6
  • Komeda, J., On the existence of Weierstrass points with a certain semigroup, Tsukuba J. Math., 6(2) (1982), 237-270.
  • Mete, P., Zengin, E.E., Minimal free resolutions of the tangent cones of Gorenstein monomial curves, Turkish Journal of Mathematics, 43 (2019), 2782-2793. https://doi.org/ 10.3906/mat-1903-15
  • Mete, P., Zengin, E.E., On minimal free resolution of the associated graded rings of certain monomial curves: new proofs in A4., Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 68(1) (2019), 1019–1029. https://doi.org/10.31801/cfsuasmas.501449
  • Sengupta, I., A minimal free resolution for certain monomial curves in A4, Comm. Algebra, 31(6) (2003), 2791–2809. https://doi.org/10.1081/AGB-120021893
  • Şahin, M., Şahin, N., On pseudo symmetric monomial curves, Communications in Algebra, 46(6) (2018), 2561-2573. https://doi.org/10.1080/00927872.2017.1392532
  • Şahin, M., Şahin, N., Betti numbers for certain Cohen-Macaulay tangent cones, Bull. Aust. Math. Soc., 99(1) (2019), 68–77. doi:10.1017/S0004972718000898
  • Stamate, D., Betti numbers for numerical semigroup rings, Multigraded Algebra and Applications-NSA 24,2016, Springer Proceedings in Mathematics and Statistics, 238 (eds.V. Ene and E. Miller) (2018)
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Nil Şahin 0000-0001-6367-6225

Yayımlanma Tarihi 30 Mart 2023
Gönderilme Tarihi 17 Mayıs 2022
Kabul Tarihi 7 Ağustos 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 72 Sayı: 1

Kaynak Göster

APA Şahin, N. (2023). Free resolutions for the tangent cones of some homogeneous pseudo symmetric monomial curves. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(1), 129-136. https://doi.org/10.31801/cfsuasmas.1117855
AMA Şahin N. Free resolutions for the tangent cones of some homogeneous pseudo symmetric monomial curves. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Mart 2023;72(1):129-136. doi:10.31801/cfsuasmas.1117855
Chicago Şahin, Nil. “Free Resolutions for the Tangent Cones of Some Homogeneous Pseudo Symmetric Monomial Curves”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, sy. 1 (Mart 2023): 129-36. https://doi.org/10.31801/cfsuasmas.1117855.
EndNote Şahin N (01 Mart 2023) Free resolutions for the tangent cones of some homogeneous pseudo symmetric monomial curves. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 1 129–136.
IEEE N. Şahin, “Free resolutions for the tangent cones of some homogeneous pseudo symmetric monomial curves”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 72, sy. 1, ss. 129–136, 2023, doi: 10.31801/cfsuasmas.1117855.
ISNAD Şahin, Nil. “Free Resolutions for the Tangent Cones of Some Homogeneous Pseudo Symmetric Monomial Curves”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/1 (Mart 2023), 129-136. https://doi.org/10.31801/cfsuasmas.1117855.
JAMA Şahin N. Free resolutions for the tangent cones of some homogeneous pseudo symmetric monomial curves. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:129–136.
MLA Şahin, Nil. “Free Resolutions for the Tangent Cones of Some Homogeneous Pseudo Symmetric Monomial Curves”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 72, sy. 1, 2023, ss. 129-36, doi:10.31801/cfsuasmas.1117855.
Vancouver Şahin N. Free resolutions for the tangent cones of some homogeneous pseudo symmetric monomial curves. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(1):129-36.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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