Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3259
Abstract
Let $K$ be a finite field and $X$ be a complete simplicial toric variety over $K$ with split torus $T_X\cong (K^*)^n$. We give an algorithm relying on elimination theory for finding generators of the vanishing ideal of a subgroup $Y_Q$ parameterized by a matrix $Q$ which can be used to study algebraic geometric codes arising from $Y_Q$. We give a method to compute the lattice $L$ whose ideal $I_L$ is exactly $I(Y_Q)$ under a mild condition. As applications, we give precise descriptions for the lattices corresponding to some special subgroups. We also prove a Nullstellensatz type theorem valid over finite fields, and share Macaulay2* codes for our algorithms.
Keywords
Evaluation code, toric variety, multigraded Hilbert function, vanishing ideal, parameterized code, lattice ideal
First Page
2141
Last Page
2150
Recommended Citation
ÖZKAN, ESMA BARAN
(2022)
"Vanishing ideals of parameterized subgroups in a toric variety,"
Turkish Journal of Mathematics: Vol. 46:
No.
6, Article 7.
https://doi.org/10.55730/1300-0098.3259
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss6/7
