Pre-publicaciones Del Seminario Matematico 2006 Generalized Principal Lattices and Cubic Pencils Generalized Principal Lattices and Cubic Pencils

Given a cubic pencil, an addition of lines can be defined in order to construct generalized principal lattices. In this paper we show the converse: the lines defining a generalized principal lattice belong to the same cubic pencil, which is unique for degrees ≥ 4.

[1]  Jesús M. Carnicer,et al.  Interpolation lattices in several variables , 2006, Numerische Mathematik.

[2]  Jesús M. Carnicer,et al.  Planar configurations with simple Lagrange interpolation formulae , 2001 .

[3]  Joe Harris,et al.  Cayley-Bacharach theorems and conjectures , 1996 .

[4]  Jesús M. Carnicer,et al.  Generation of lattices of points for bivariate interpolation , 2004, Numerical Algorithms.

[5]  Jesús M. Carnicer,et al.  A conjecture on multivariate polynomial interpolation. , 2001 .

[6]  Y. E. Muneer.  On lagrange and hermite interpolation. I , 1987 .

[7]  K. Chung,et al.  On Lattices Admitting Unique Lagrange Interpolations , 1977 .

[8]  C. Hoffmann.  Algebraic curves , 1988 .

[9]  Jesús M. Carnicer,et al.  Interpolation on lattices generated by cubic pencils , 2006, Adv. Comput. Math..

[10]  Robert Bix,et al.  Conics and Cubics: A Concrete Introduction to Algebraic Curves , 1998 .

[11]  B. M. Fulk.  MATH , 1992 .

[12]  J. M. Carnicer,et al.  Pre-publicaciones Del Seminario Matematico 2001 , 2022 .

[13]  R. A. Nicolaides,et al.  On a Class of Finite Elements Generated by Lagrange Interpolation , 1972 .

[14]  Jesús M. Carnicer,et al.  Geometric characterization and generalized principal lattices , 2006, J. Approx. Theory.

[15]  J. Carnicer,et al.  On Chung and Yao's geometric characterization for bivariate polynomial interpolation , 2002 .

[16]  J. R. Busch,et al.  A note on Lagrange interpolation in R2 , 1990 .

[17]  S. L. Lee,et al.  Construction of lattices for lagrange interpolation in projective space , 1991 .