On minimal free resolution of the associated graded rings of certain monomial curves : New proofs in A⁴
Abstract
In this article, even if it is known for general case in <cite>sharifan-nahandi</cite>, we give the explicit minimal free resolution of the associated graded ring of certain affine monomial curves in affine 4-space based on the standard basis theory. As a result, we give the minimal graded free resolution and the Hilbert function of the tangent cone of these families in A⁴ in the simple form according to <cite>sharifan-nahandi</cite>.
Keywords
Minimal free resolution monomial curve Cohen-Macaulayness Hilbert function of a local ring tangent cone
References
- Arslan, S.F., Cohen-Macaulayness of tangent cones, Proc. Amer. Math. Soc. 128 (2000) 2243-2251.
- Barucci, V.,Fröberg, R. and Şahin, M., On free resolutions of some semigroup rings, J. Pure and Appl. Algebra 218 (6) (2014) 1107-1116.
- Buchsbaum, D. and Eisenbud, D., What makes a complex exact?, Journal of Algebra 25 (1973) 259-268.
- Gimenez, P., Sengupta, I. andSrinivasan, H., Minimal free resolutions for certain affine monomial curves, Contemporary Mathematics 555 (2011) 87-95.
- Greuel, G-M, Pfister, G., A Singular Introduction to Commutative Algebra, Springer-Verlag, 2002.
- Decker, W., Greuel, G-M., Pfister, G., and Schönemann, H., Singular {4-1-0} - A computer algebra system for polynomial computations. http://www.singular.uni-kl.de (2016).
- Molinelli, S. and Tamone, G., On the Hilbert function of certain rings of monomial curves, J. Pure and Appl. Algebra 101 (2) (1995) 191-206.
- Molinelli, S. and Tamone, G., On the Hilbert function of certain non-Cohen-Macaulay one dimensional rings, Rocky Mountain J. Math. 29 (1) (1999) 271-300.
- Molinelli, S., Patil, D.P. and Tamone, G., On the Cohen-Macaulayness of the associated graded ring of certain monomial curves. Beitrage Algebra Geom. 39 (2) (1998) 433-446.
- Oneto, A. and Tamone, G., Explicit minimal resolution for certain monomial curves, arXiv:1312.0789 [math.AC].
- Patil, D.P., Minimal sets of generators for the relation ideals of certain monomial curves, Manuscripta Math. 80 (1993) 239-248.
- Rossi, M., Hilbert functions of Cohen-Macaulay local rings, Commutative Algebra and its Connections to Geometry, Contemporary Math 555 (2011) 173-200.
- Rossi, M.E. and Sharifan, L., Minimal free resolution of a finitely generated module over a regular local ring, Journal of Algebra 322 (10) (2009) 3693-3712.
- Rossi, M.E. and Valla, G., Hilbert functions of filtered modules, Lecture Notes the Unione Matematica Italiana 9, Springer, 2010.
- Sengupta, I., A minimal free resolution for certain monomial curves in A⁴, Comm. in Algebra 31 (6) (2003) 2791-2809.
- Sengupta, I., A Gröbner basis for certain affine monomial curves, Comm. in Algebra 31 (3) (2003) 1113-1129.
- Sharifan, L. and Zaare-Nahandi, R., Minimal free resolution of the associated graded ring of monomial curves of generalized arithmetic sequences, J. of Pure and Appl. Algebra 213 (2009) 360-369.
Abstract
References
- Arslan, S.F., Cohen-Macaulayness of tangent cones, Proc. Amer. Math. Soc. 128 (2000) 2243-2251.
- Barucci, V.,Fröberg, R. and Şahin, M., On free resolutions of some semigroup rings, J. Pure and Appl. Algebra 218 (6) (2014) 1107-1116.
- Buchsbaum, D. and Eisenbud, D., What makes a complex exact?, Journal of Algebra 25 (1973) 259-268.
- Gimenez, P., Sengupta, I. andSrinivasan, H., Minimal free resolutions for certain affine monomial curves, Contemporary Mathematics 555 (2011) 87-95.
- Greuel, G-M, Pfister, G., A Singular Introduction to Commutative Algebra, Springer-Verlag, 2002.
- Decker, W., Greuel, G-M., Pfister, G., and Schönemann, H., Singular {4-1-0} - A computer algebra system for polynomial computations. http://www.singular.uni-kl.de (2016).
- Molinelli, S. and Tamone, G., On the Hilbert function of certain rings of monomial curves, J. Pure and Appl. Algebra 101 (2) (1995) 191-206.
- Molinelli, S. and Tamone, G., On the Hilbert function of certain non-Cohen-Macaulay one dimensional rings, Rocky Mountain J. Math. 29 (1) (1999) 271-300.
- Molinelli, S., Patil, D.P. and Tamone, G., On the Cohen-Macaulayness of the associated graded ring of certain monomial curves. Beitrage Algebra Geom. 39 (2) (1998) 433-446.
- Oneto, A. and Tamone, G., Explicit minimal resolution for certain monomial curves, arXiv:1312.0789 [math.AC].
- Patil, D.P., Minimal sets of generators for the relation ideals of certain monomial curves, Manuscripta Math. 80 (1993) 239-248.
- Rossi, M., Hilbert functions of Cohen-Macaulay local rings, Commutative Algebra and its Connections to Geometry, Contemporary Math 555 (2011) 173-200.
- Rossi, M.E. and Sharifan, L., Minimal free resolution of a finitely generated module over a regular local ring, Journal of Algebra 322 (10) (2009) 3693-3712.
- Rossi, M.E. and Valla, G., Hilbert functions of filtered modules, Lecture Notes the Unione Matematica Italiana 9, Springer, 2010.
- Sengupta, I., A minimal free resolution for certain monomial curves in A⁴, Comm. in Algebra 31 (6) (2003) 2791-2809.
- Sengupta, I., A Gröbner basis for certain affine monomial curves, Comm. in Algebra 31 (3) (2003) 1113-1129.
- Sharifan, L. and Zaare-Nahandi, R., Minimal free resolution of the associated graded ring of monomial curves of generalized arithmetic sequences, J. of Pure and Appl. Algebra 213 (2009) 360-369.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Submission Date | December 22, 2017 |
| Acceptance Date | June 18, 2018 |
| Publication Date | February 1, 2019 |
| DOI | https://doi.org/10.31801/cfsuasmas.501449 |
| IZ | https://izlik.org/JA44NT38XM |
| Published in Issue | Year 2019 Volume: 68 Issue: 1 |
Cite
Cited By
Free resolutions for the tangent cones of some homogeneous pseudo symmetric monomial curves
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
https://doi.org/10.31801/cfsuasmas.1117855
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
