Binomial vanishing ideals

Authors

Azucena Tochimani Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14–740, 07000 Mexico City, D.F. ROR
Rafael H. Villarreal Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14–740, 07000 Mexico City, D.F. ROR https://orcid.org/0000-0001-9473-765X

Vanishing ideal, Binomial ideal, Monomial parameterization, Projective variety

In this note we characterize, in algebraic and geometric terms, when a graded vanishing ideal is generated by binomials over any field $K$.

Received: 9 March 2015 | Accepted: 22 April 2015

Download data is not yet available.

D. Cox, J. Little, and D. O’Shea, Ideals, Varieties, and Algorithms, Springer-Verlag, New York (1992).

D. Eisenbud and B. Sturmfels, Binomial ideals, Duke Math. J. 84(1) (1996) 1-45.

M. Gasca and T. Sauer, Polynomial interpolation in several variables, Adv. Comput. Math. 12(4) (2000) 377-410.

M. González-Sarabia, C. Rentería, and H. Tapia-Recillas, Reed-Muller-type codes over the Segre variety, Finite Fields Appl. 8(4) (2002) 511-518.

J. Harris, Algebraic Geometry: A First Course, Graduate Texts in Mathematics 133, Springer-Verlag, New York (1992).

M. Hellus and R. Waldi, Interpolation in affine and projective space over a finite field, J. Commut. Algebra 7(2) (2015) 207-221.

N. Jacobson, Basic Algebra I, 2nd Edition, W. H. Freeman and Company, New York (1996).

H. H. López, C. Rentería, and R. H. Villarreal, Affine cartesian codes, Des. Codes Cryptogr. 71(1) (2014) 5-19.

J. Neves, M. Vaz Pinto, and R. H. Villarreal, Regularity and algebraic properties of certain lattice ideals, Bull. Braz. Math. Soc. (N.S.) 45(4) (2014) 777-806.

L. O’Carroll, F. Planas-Vilanova, and R. H. Villarreal, Degree and algebraic properties of lattice and matrix ideals, SIAM J. Discrete Math. 28(1) (2014) 394-427.

A. Tochimani and R. H. Villarreal, Vanishing ideals over rational parameterizations, Math. Notes 105(3) (2019) 441-454.

R. H. Villarreal, Monomial Algebras, 2nd Edition, Monographs and Research Notes in Mathematics, CRC Press (2015).