# Toric ideals for high Veronese subrings of toric algebras - Mathematics > Commutative Algebra

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Abstract: We prove that the defining ideal of a sufficiently high Veronese subring of atoric algebra admits a quadratic Gr\-obner basis consisting of binomials. Moregenerally, we prove that the defining ideal of a sufficiently high Veronesesubring of a standard graded ring admits a quadratic Gr\-obner basis. We give alower bound on $d$ such that the defining ideal of $d$-th Veronese subringadmits a quadratic Gr\-obner basis. Eisenbud-Reeves-Totaro stated the sametheorem without a proof with some lower bound on $d$. In many cases, our lowerbound is less than Eisenbud-Reeves-Totaro-s lower bound.

Author: ** Takafumi Shibuta**

Source: https://arxiv.org/