Montoro López, M. EulàliaMoner i Farran, Berta2023-10-252023-10-252023-06-12https://hdl.handle.net/2445/203140Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: M. Eulàlia Montoro López[en] In this work, the $\mu$-bases of plane rational curves are shown from the point of view of algebraic geometry and algebraic varieties. Thus, the Gröbner bases are previously presented, which are of great importance in this area but more expensive than the $\mu$ bases. Based on the definition and construction of the latter, two applications are shown: modules and implication, both polynomial and rational. The work is based on the article The moving line ideal basis of planar rational curves from Cox, D.A, Sederberg, T.W., Chen, F. published on 1998 by Computer Aided Geometry Design 15.61 p.application/pdfcatcc-by-nc-nd (c) Berta Moner i Farran, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/Corbes el·líptiquesVarietats abelianesGeometria algebraicaTreballs de fi de grauElliptic curvesAbelian varietiesAlgebraic geometryBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess