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arXiv · 0906.5129

Toric ideals for high Veronese subrings of toric algebras

Takafumi Shibuta
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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.

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Takafumi Shibuta. 2010-11-19. Toric ideals for high Veronese subrings of toric algebras. https://arxiv.org/abs/0906.5129

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