Binomial vanishing ideals

Abstract

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

Keywords

• Vanishing ideal, Binomial ideal, Monomial parameterization, Projective variety

Binomial vanishing ideals

Abstract

References

1. D. Cox, J. Little and D. O’Shea, Ideals, varieties, and algorithms, Springer-Verlag, 1992.
2. D. Eisenbud and B. Sturmfels, Binomial ideals, Duke Math. J., 84(1), 1-45, 1996.
3. M. Gasca and T. Sauer, Polynomial interpolation in several variables, Adv. Comput. Math., 12(4), 377-410, 2000.
4. M. González-Sarabia, C. Rentería and H. Tapia-Recillas, Reed-Muller-type codes over the Segre va- riety, Finite Fields Appl., 8(4), 511-518, 2002.
5. J. Harris, Algebraic geometry: A first course, Graduate Texts in Mathematics 133, Springer-Verlag, New York, 1992.
6. M. Hellus and R. Waldi, Interpolation in affine and projective space over a finite field, J. Commut. Algebra, to appear. N. Jacobson, Basic algebra I , Second Edition, W. H. Freeman and Company, New York, 1996.
7. H. H. López, C. Rentería and R. H. Villarreal, Affine cartesian codes, Des. Codes Cryptogr., 71(1), 5-19, 2014.
8. 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), 777-806, 2014.

9. 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), 394-427, 2014.
10. A. Tochimani and R. H. Villarreal, Vanishing ideals over rational parameterizations, preprint, arXiv:1502.05451v1, 2015.
11. R. H. Villarreal, Monomial algebras, second edition, Monographs and Research Notes in Mathematics, CRC Press, 2015.