Minimal Generators of the Defining Ideal of the Rees Algebra Associated with a Rational Plane Parametrization with μ = 2
Canadian journal of mathematics, Tome 66 (2014) no. 6, pp. 1225-1249

Voir la notice de l'article provenant de la source Cambridge University Press

We exhibit a set of minimal generators of the defining ideal of the Rees Algebra associated with the ideal of three bivariate homogeneous polynomials parametrizing a proper rational curve in projective plane, having a minimal syzygy of degree 2.
DOI : 10.4153/CJM-2013-035-1
Mots-clés : 13A30, 14H50, Rees Algebras, rational plane curves, minimal generators
Benítez, Teresa Cortadellas; D'Andrea, Carlos. Minimal Generators of the Defining Ideal of the Rees Algebra Associated with a Rational Plane Parametrization with μ = 2. Canadian journal of mathematics, Tome 66 (2014) no. 6, pp. 1225-1249. doi: 10.4153/CJM-2013-035-1
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[BH93] [BH93] Bruns, W. and Herzog, J., Cohen-Macaulay rings. Cambridge Studies in Advanced Mathematics, 39, Cambridge University Press, Cambridge, 1993. Google Scholar

[Bus09] [Bus09] Busé, L., On the equations of the moving curve ideal of a rational algebraic plane curve. J. Algebra. 321(2009), no. 8, 2317–2344. Google Scholar | DOI

[BJ03] [BJ03] Busé, L. and Jouanolou, J.-P., On the closed image of a rational map and the implicitization problem. J. Algebra. 265(2003), no. 1, 312–357. Google Scholar | DOI

[CA00] [CA00] Casas-Alvero, E., Singularities of plane curves. London Mathematical Society Lecture Note Series, 276, Cambridge University Press, Cambridge, 2000. Google Scholar

[CCL05] [CCL05] Chen, F., Cox, D., and Liu, Y., The μ-basis and implicitization of a rational parametric surface. J. Symbolic Comput. 39(2005), no. 6, 689–706. Google Scholar | DOI

[CWL08] [CWL08] Chen, F., Wang, W. , and Liu, Y., Computing singular points of plane rational curves. J. Symbolic Comput. . 43(2008), no. 2, 92–117. Google Scholar | DOI

[CD10] [CD10] Cortadellas Benítez, T. and D'Andrea, C., Minimal generators of the defining ideal of the Rees Algebra associated to monoid parametrizations. Comput. Aided Geom. Design. 27(2010), no. 6, 461–473. Google Scholar | DOI

[CD13] [CD13] Cortadellas Benítez, T. and D'Andrea, C., Rational plane curves parametrizable by conics. J. Algebra. 373(2013) 453–480. Google Scholar | DOI

[CD13b] [CD13b] Cortadellas Benítez, T. and D'Andrea, C., Minimal generators of the defining ideal of the Rees Algebra associated to a rational plane parameterization with μ= 2. arxiv:1301.6286 Google Scholar

[Cox08] [Cox08] Cox, D. A., The moving curve ideal and the Rees algebra. Theoret. Comput. Sci. 392(2008), no. 1–3, 23–36. Google Scholar | DOI

[CGZ00] [CGZ00] Cox, D., Goldman, R., and Zhang, M. , On the validity of implicitization by moving quadrics of rational surfaces with no base points. J. Symbolic Comput. 29(2000), no. 3, 419–440. Google Scholar | DOI

[CHW08] [CHW08] Cox, D., Hoffman, J. W., and Wang, H., Syzygies and the Rees algebra. J. Pure Appl. Algebra. 212(2008), no. 7, 1787–1796. Google Scholar | DOI

[CKPU11] [CKPU11] Cox, D., Kustin, A., Polini, C., and Ulrich, B., A study of singularities on rational curves via syzygies. Mem. Amer. Math. Soc. 222(2013), no. 1045. Google Scholar

[CLO07] [CLO07] Cox, D., Little, J., and O'Shea, D., Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra. Third ed., Undergraduate Texts in Mathematics, Springer, New York, 2007. Google Scholar

[CSC98] [CSC98] Cox, D. A., Sederberg, T. W., and Chen, F., The moving line ideal basis of planar rational curves. Comput. Aided Geom. Design. 15(1998), no. 8, 803–827. Google Scholar | DOI

[Mac] [Mac] Grayson, D. R. and Stillman, M. E., Macaulay 2, a software system for research in algebraic geometry. http://www.math.uiuc.edu/Macaulay2/. Google Scholar

[HS12] [HS12] Hassanzadeh, S. H. and Simis, A. , Implicitization of the Jonquières parametrizations. arxiv:1205.1083. Google Scholar

[HSV08] [HSV08] Hong, J., Simis, A., and Vasconcelos, W. V., On the homology of two-dimensional elimination. J. Symbolic Comput. 43(2008), no. 4, 275–292. Google Scholar | DOI

[HSV09] [HSV09] Hong, J., Simis, A., and Vasconcelos, W. V., The equations of almost complete intersections. Bull. Braz. Math. Soc. 43(2012), no. 2, 171–199. Google Scholar

[HW10] [HW10] Hoffman, J. W. and Wang, H., Defining equations of the Rees algebra of certain parametric surfaces. J. Algebra Appl. 9(2010), no. 6, 1033–1049. Google Scholar | DOI

[Jou97] [Jou97] Jouanolou, J. P., Formes d'inertie et résultant: un formulaire. Adv. Math. 126(1997), no. 2, 119–250. Google Scholar | DOI

[KPU09] [KPU09] Kustin, A. R., Polini, C., and Ulrich, B., Rational normal scrolls and the defining equations of Rees algebras. J. Reine Angew. Math. 650(2011), 23–65. Google Scholar

[KPU13] [KPU13] Kustin, A. R., Polini, C., and Ulrich, B., The bi-graded structure of symmetric algebras with applications to Rees rings. arxiv:1301.7106 Google Scholar

[SC95] [SC95] Sederberg, T. and Chen, F., Implicitization using moving curves and surfaces. Proceedings of SIGGRAPH. 1995, 301–308. Google Scholar

[SGD97] [SGD97] Sederberg, T., Goldman, R., and Du, H., Implicitizing rational curves by the method of moving algebraic curves. In: Parametric algebraic curves and applications (Albuquerque, NM, 1995) J. Symbolic Comput. 23(1997), no. 2–3, 153–175. Google Scholar | DOI

[SWP08] [SWP08] Sendra, J. R., Winkler, F., and Pérez-Díaz, S., Rational algebraic curves. A computer algebra approach. Algorithms and Computation in Mathematics, 22, Springer, Berlin, 2008. Google Scholar

[Wol10] [Wol10] Wolfram Research, Inc. Mathematica, Version 8.0, Champaign, IL, 2010. Google Scholar

[ZCG99] [ZCG99] Zhang, M., Chionh, E.-W., and Goldman, R. N., On a relationship between the moving line and moving conic coefficient matrices. Comput. Aided Geom. Design 16(1999), no. 6, 517–527. Google Scholar | DOI

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