Toric ideals for high Veronese subrings of toric algebras

Details Toric ideals for high Veronese subrings of toric algebras Toric ideals for high Veronese subrings of toric algebras

2009-06-29

arxiv.org/abs/0906.5129v3

Mathematics

Commutative Algebra

9 pages, v2: Observation 3.16 added and typos corrected, v3: typos corrected

Scientific paper

We prove that the defining ideal of a sufficiently high Veronese subring of a toric algebra admits a quadratic Gr\"obner 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 Gr\"obner basis. We give a lower bound on $d$ such that the defining ideal of $d$-th Veronese subring admits a quadratic Gr\"obner 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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