Toric ideals for high Veronese subrings of toric algebras

Takafumi Shibuta

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    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 dth 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. 2013

    Original languageEnglish
    Pages (from-to)895-905
    Number of pages11
    JournalIllinois Journal of Mathematics
    Volume55
    Issue number3
    DOIs
    Publication statusPublished - 2011

    All Science Journal Classification (ASJC) codes

    • Mathematics(all)

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