Abstract
We prove that the defining ideal of a sufficiently high Veronese subring of a toric algebra admits a quadratic Gröbner basis consisting of binomials. More generally, we prove that the defining ideal of a sufficiently high Veronese subring of a standard graded ring admits a quadratic Gröbner basis. We give a lower bound on $d$ such that the defining ideal of $d$th Veronese subring admits a quadratic Gröbner basis. Eisenbud–Reeves–Totaro stated the same theorem without a proof with some lower bound on $d$. In many cases, our lower bound is less than Eisenbud–Reeves–Totaro’s lower bound.
Citation
Takafumi Shibuta. "Toric ideals for high Veronese subrings of toric algebras." Illinois J. Math. 55 (3) 895 - 905, Fall 2011. https://doi.org/10.1215/ijm/1369841790
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